%PDF-1.2 3 0 obj << /Length 4 0 R >> stream 1 0 0 1 136.63 708.12 cm BT /F15 19.83 Tf 0 0 Td[(Industrial)-418(Strength)-417(F)35(acto)34(rization)]TJ 81.43 -99.9 Td[(La)34(wren)-417(Smithline)]TJ -0.58 -27.89 Td[(Co)35(rnell)-416(Universit)36(y)]TJ/F16 19.83 Tf -32.65 -27.9 Td[(lawren@math.cornell.edu)]TJ -63.21 -27.89 Td[(http://www.math.cornell.edu/~l)-10(awren)]TJ ET endstream endobj 4 0 obj 329 endobj 1 0 obj << /Font << /F15 5 0 R /F16 6 0 R >> /ProcSet [/PDF /Text] >> endobj 2 0 obj << /Type /Page /Contents 3 0 R /Resources 1 0 R /MediaBox [0 0 595.27 841.89] /Parent 7 0 R >> endobj 10 0 obj << /Length 11 0 R >> stream 1 0 0 1 140.76 648.67 cm BT /F15 19.83 Tf 0 0 Td[(Industrial)-418(Strength)-417(F)35(acto)34(rization)]TJ -68.38 -57.79 Td[(Given)-416(an)-417(integer)]TJ/F19 19.83 Tf 174.91 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(,)]TJ -193.75 -57.78 Td[(determine)-416(the)-417(p)35(rime)-416(diviso)35(rs)-417(of)]TJ/F19 19.83 Tf 322.69 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(.)]TJ -341.53 -85.68 Td[(De\014nition.)-555(An)-417(integer)]TJ/F19 19.83 Tf 231.24 0 Td[(p)]TJ/F15 19.83 Tf 18.87 0 Td[(is)-417(p)35(rime)-416(means:)]TJ -250.11 -57.78 Td[(1)]TJ/F19 19.83 Tf 12.39 0 Td[(=p)]TJ/F15 19.83 Tf 29.41 0 Td[(is)-417(not)-417(an)-417(integer,)-417(and)]TJ -41.8 -57.78 Td[(fo)35(r)-417(integers)]TJ/F19 19.83 Tf 123.12 0 Td[(a;)-178(b)]TJ/F15 19.83 Tf 29.58 0 Td[(,)]TJ -152.7 -57.79 Td[(if)]TJ/F19 19.83 Tf 21.34 0 Td[(p)]TJ/F22 19.83 Tf 16.46 0 Td[(j)]TJ/F19 19.83 Tf 11.71 0 Td[(ab)]TJ/F15 19.83 Tf 20.21 0 Td[(,)-417(then)]TJ/F19 19.83 Tf 68.17 0 Td[(p)]TJ/F22 19.83 Tf 16.46 0 Td[(j)]TJ/F19 19.83 Tf 11.71 0 Td[(a)]TJ/F15 19.83 Tf 19.46 0 Td[(o)35(r)]TJ/F19 19.83 Tf 28.23 0 Td[(p)]TJ/F22 19.83 Tf 16.46 0 Td[(j)]TJ/F19 19.83 Tf 11.71 0 Td[(b)]TJ/F15 19.83 Tf 9.01 0 Td[(.)]TJ ET endstream endobj 11 0 obj 1171 endobj 8 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 9 0 obj << /Type /Page /Contents 10 0 R /Resources 8 0 R /MediaBox [0 0 595.27 841.89] /Parent 7 0 R >> endobj 16 0 obj << /Length 17 0 R >> stream 1 0 0 1 140.76 646.6 cm BT /F15 19.83 Tf 0 0 Td[(Industrial)-418(Strength)-417(F)35(acto)34(rization)]TJ -68.38 -57.78 Td[(Application:)]TJ 0 -27.89 Td[(b)35(reak)-417(certain)-416(public)-417(k)35(ey)-416(cryp)35(rography)105(.)]TJ 0 -57.79 Td[(Metap)34(roblem)-416(I:)-417(Ho)35(w)-418(much)-416(do)-35(es)-417(it)-417(cost)-417(to)]TJ 0 -27.89 Td[(facto)34(r)-416(a)]TJ/F19 19.83 Tf 87.45 0 Td[(d)]TJ/F15 19.83 Tf 19.11 0 Td[(digit)-417(numb)-35(er)]TJ/F19 19.83 Tf 137.72 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(?)]TJ -263.12 -57.79 Td[(Metap)34(roblem)-403(I)-35(I:)-404(Given)]TJ/F19 19.83 Tf 233.19 0 Td[(d)]TJ/F15 19.83 Tf 10.85 0 Td[(,)-406(design)-403(a)-404(strategy)-404(fo)35(r)]TJ -244.04 -27.89 Td[(picking)]TJ/F19 19.83 Tf 78.7 0 Td[(N)]TJ/F15 19.83 Tf 26.62 0 Td[(which)-392(maximizes)-393(the)-392(cost)-393(to)-392(facto)34(r.)]TJ -105.32 -57.78 Td[(Metap)34(roblem)-331(I)-35(I)-35(I:)-332(Given)-331(a)-332(determined)]TJ/F32 19.83 Tf 373.04 0 Td[(adversa)35(ry)]TJ/F15 19.83 Tf -373.04 -27.9 Td[(who)-409(has)-409(solved)-408(Metap)35(roblem)-408(I)-36(I)-408(and)-409(who)-409(picks)]TJ/F19 19.83 Tf 0 -27.89 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(,)-417(ho)34(w)-417(much)-417(do)-35(es)-416(it)-417(cost)-417(to)-417(facto)34(r)]TJ/F19 19.83 Tf 351.62 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(?)]TJ ET endstream endobj 17 0 obj 1316 endobj 14 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F32 18 0 R >> /ProcSet [/PDF /Text] >> endobj 15 0 obj << /Type /Page /Contents 16 0 R /Resources 14 0 R /MediaBox [0 0 595.27 841.89] /Parent 7 0 R >> endobj 21 0 obj << /Length 22 0 R >> stream 1 0 0 1 233.62 706.52 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ast)-417(and)-418(Slo)36(w)]TJ -161.24 -57.78 Td[(De\014nition)-466(\050fo)34(r)-467(to)-35(da)34(y\051)-466(A)-467(fast)-468(algo)35(rithm)-468(is)-467(one)]TJ 0 -27.89 Td[(which)-394(runs)-393(in)-394(p)-35(olynomial)-394(time)-394(in)-393(the)-394(length)-394(of)]TJ 0 -27.9 Td[(its)-417(input.)]TJ 0 -57.78 Td[(Example.)-1030(Multiplication)-575(of)-575(t)34(w)34(o)-575(numb)-35(ers)]TJ/F19 19.83 Tf 439.69 0 Td[(N)]TJ/F17 16.53 Tf 16.72 -4.07 Td[(1)]TJ/F15 19.83 Tf -456.41 -23.83 Td[(and)]TJ/F19 19.83 Tf 44.76 0 Td[(N)]TJ/F17 16.53 Tf 16.72 -4.07 Td[(2)]TJ/F15 19.83 Tf 19.09 4.07 Td[(each)-417(with)-417(at)-418(most)]TJ/F19 19.83 Tf 193.37 0 Td[(d)]TJ/F15 19.83 Tf 19.11 0 Td[(digits.)]TJ -293.05 -57.78 Td[(ab)-35(out)-278(2)]TJ/F19 19.83 Tf 76.43 0 Td[(d)]TJ/F17 16.53 Tf 10.85 7 Td[(2)]TJ/F15 19.83 Tf 16.33 -7 Td[(op)-35(erations,)-306(dep)-35(ending)-277(ho)34(w)-278(y)35(ou)-278(count.)]TJ 129.25 -86.67 Td[(1)-804(3)-804(7)]TJ/F22 19.83 Tf -32.33 -23.92 Td[()]TJ/F15 19.83 Tf 60.67 0 Td[(3)-804(7)]TJ ET -3.9 -375.19 152.56 0.6 re f 1 0 0 1 99.96 -392.12 cm BT /F15 19.83 Tf 0 0 Td[(4)-804(9)]TJ -28.34 -23.91 Td[(2)-804(1)]TJ 0 -23.91 Td[(2)-804(1)]TJ 0 -23.91 Td[(9)]TJ 0 -23.91 Td[(7)]TJ -67.55 -23.91 Td[(+)-1006(3)]TJ ET -103.86 -127.13 152.56 0.6 re f 1 0 0 1 -56.67 -144.06 cm BT /F15 19.83 Tf 0 0 Td[(5)-804(0)-804(6)-804(9)]TJ ET endstream endobj 22 0 obj 1413 endobj 19 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F17 5 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 20 0 obj << /Type /Page /Contents 21 0 R /Resources 19 0 R /MediaBox [0 0 595.27 841.89] /Parent 7 0 R >> endobj 25 0 obj << /Length 26 0 R >> stream 1 0 0 1 233.62 619.83 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ast)-417(and)-418(Slo)36(w)]TJ -161.24 -57.78 Td[(F)35(ast)-418(examples:)]TJ 0 -57.78 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[(N)]TJ/F15 19.83 Tf 27.1 0 Td[(b)-35(e)-416(a)]TJ/F19 19.83 Tf 52.34 0 Td[(d)]TJ/F15 19.83 Tf 19.1 0 Td[(digit)-417(integer.)]TJ -140.82 -57.79 Td[(W)35(rite)]TJ/F19 19.83 Tf 64.18 0 Td[(N)]TJ/F15 19.83 Tf 27.1 0 Td[(on)-417(the)-417(b)-34(oa)34(rd:)]TJ/F19 19.83 Tf 157.01 0 Td[(O)]TJ/F15 19.83 Tf 16.57 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(d)]TJ/F15 19.83 Tf 10.84 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -294.98 -57.78 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(a)-296(<)-294(N)]TJ/F15 19.83 Tf 58.12 0 Td[(,)-417(compute)]TJ/F19 19.83 Tf 110.87 0 Td[(N)-107(a)]TJ/F15 19.83 Tf 30.03 0 Td[(:)]TJ/F19 19.83 Tf 26.17 0 Td[(O)]TJ/F15 19.83 Tf 16.58 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(d)]TJ/F17 16.53 Tf 10.84 7 Td[(2)]TJ/F15 19.83 Tf 10.83 -7 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -325 -57.78 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(a)-296(<)-294(N)]TJ/F15 19.83 Tf 58.12 0 Td[(,)-417(compute)]TJ/F19 19.83 Tf 110.87 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.72 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(N)-48(;)-177(a)]TJ/F15 19.83 Tf 38.22 0 Td[(\051:)]TJ/F19 19.83 Tf 35.81 0 Td[(O)]TJ/F15 19.83 Tf 16.58 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(d)]TJ/F17 16.53 Tf 10.84 7 Td[(3)]TJ/F15 19.83 Tf 10.83 -7 Td[(\051.)]TJ ET endstream endobj 26 0 obj 1440 endobj 23 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F17 5 0 R >> /ProcSet [/PDF /Text] >> endobj 24 0 obj << /Type /Page /Contents 25 0 R /Resources 23 0 R /MediaBox [0 0 595.27 841.89] /Parent 7 0 R >> endobj 29 0 obj << /Length 30 0 R >> stream 1 0 0 1 233.62 640.63 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ast)-417(and)-418(Slo)36(w)]TJ -161.24 -57.79 Td[(What)-417(is)-417(slo)35(w?)]TJ 0 -57.78 Td[(F)35(acto)34(r)-416(an)-418(o)-34(dd)-417(integer)]TJ/F19 19.83 Tf 230.27 0 Td[(N)]TJ/F15 19.83 Tf 27.11 0 Td[(b)35(y)-416(trial)-417(division.)]TJ -257.38 -85.68 Td[(Example)]TJ/F19 19.83 Tf 94.61 0 Td[(N)]TJ/F15 19.83 Tf 24.7 0 Td[(=)-295(209.)]TJ -109.35 -51.57 Td[(try)-416(3)]TJ 0 -23.91 Td[(try)-416(5)]TJ 0 -23.91 Td[(try)-416(7)]TJ 0 -23.91 Td[(try)-416(9)]TJ 0 -23.91 Td[(try)-416(11)-417(!)]TJ ET endstream endobj 30 0 obj 557 endobj 27 0 obj << /Font << /F15 5 0 R /F19 12 0 R >> /ProcSet [/PDF /Text] >> endobj 28 0 obj << /Type /Page /Contents 29 0 R /Resources 27 0 R /MediaBox [0 0 595.27 841.89] /Parent 7 0 R >> endobj 33 0 obj << /Length 34 0 R >> stream 1 0 0 1 233.62 676.49 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ast)-417(and)-418(Slo)36(w)]TJ -161.24 -57.78 Td[(T)104(o)-416(facto)34(r)]TJ/F19 19.83 Tf 103.84 0 Td[(N)]TJ/F15 19.83 Tf 27.1 0 Td[(with)]TJ/F19 19.83 Tf 51.65 0 Td[(d)]TJ/F15 19.83 Tf 19.11 0 Td[(digits)]TJ -201.7 -57.78 Td[(b)35(y)-370(trial)-370(division,)-380(w)35(e)-370(ma)34(y)-370(have)-370(to)-370(go)-371(up)-370(to)]TJ/F22 19.83 Tf 423.96 16.67 Td[(p)]TJ ET 280.28 -98.89 18.84 0.89 re f 1 0 0 1 280.28 -115.56 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(,)]TJ -460.36 -27.9 Td[(which)-417(has)-417(ab)-35(out)]TJ/F19 19.83 Tf 174.77 0 Td[(d=)]TJ/F15 19.83 Tf 21.38 0 Td[(2)-417(digits.)]TJ -196.15 -57.78 Td[(Slo)36(w)-418(example:)]TJ/F19 19.83 Tf 155.63 0 Td[(O)]TJ/F15 19.83 Tf 16.57 0 Td[(\050)]TJ/F22 19.83 Tf 9.64 16.67 Td[(p)]TJ ET -242.12 -69.01 18.84 0.89 re f 1 0 0 1 -242.12 -85.68 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051)-295(=)]TJ/F19 19.83 Tf 40.63 0 Td[(O)]TJ/F15 19.83 Tf 16.57 0 Td[(\050exp\050)]TJ/F19 19.83 Tf 53.72 0 Td[(d=)]TJ/F15 19.83 Tf 21.38 0 Td[(2\051\051)]TJ/F19 19.83 Tf 31.67 0 Td[(:)]TJ/F15 19.83 Tf -382.21 -57.79 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(d)]TJ/F15 19.83 Tf 16.69 0 Td[(=)-296(150,)-417(at)-417(sp)-36(eed)-416(of)-416(10)]TJ/F17 16.53 Tf 224.7 7 Td[(9)]TJ/F15 19.83 Tf 19.1 -7 Td[(trials)-417(/)-417(second,)]TJ -302.77 -27.89 Td[(trial)-417(division)-416(p)-35(otentially)-417(tak)34(es)-417(10)]TJ/F17 16.53 Tf 330.26 7 Td[(66)]TJ/F15 19.83 Tf 29.43 -7 Td[(seconds.)]TJ -359.69 -57.78 Td[(One)-417(y)35(ea)35(r)-416(is)]TJ/F19 19.83 Tf 122.99 0 Td[()]TJ/F22 19.83 Tf 17.49 0 Td[()]TJ/F15 19.83 Tf 10.54 0 Td[(10)]TJ/F17 16.53 Tf 24.79 7 Td[(7)]TJ/F15 19.83 Tf 19.09 -7 Td[(seconds.)]TJ/F19 19.83 Tf -194.9 -57.79 Td[()]TJ/F15 19.83 Tf 18.66 0 Td[(=)]TJ/F22 19.83 Tf 25.14 16.45 Td[(p)]TJ ET -138.04 -184.8 24.79 0.89 re f 1 0 0 1 -138.04 -201.25 cm BT /F15 19.83 Tf 0 0 Td[(10.)]TJ/F19 19.83 Tf -61.36 -57.78 Td[()]TJ/F22 19.83 Tf 17.49 0 Td[()]TJ/F15 19.83 Tf 10.54 0 Td[(10)]TJ/F17 16.53 Tf 24.79 7 Td[(58)]TJ/F15 19.83 Tf 29.42 -7 Td[(y)35(ea)35(rs)-417(is)-417(a)-417(long)-416(time.)]TJ ET endstream endobj 34 0 obj 2163 endobj 31 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F17 5 0 R >> /ProcSet [/PDF /Text] >> endobj 32 0 obj << /Type /Page /Contents 33 0 R /Resources 31 0 R /MediaBox [0 0 595.27 841.89] /Parent 35 0 R >> endobj 38 0 obj << /Length 39 0 R >> stream 1 0 0 1 238.79 657.69 cm BT /F15 19.83 Tf 0 0 Td[(T)104(rial)-416(Division)]TJ -166.41 -57.78 Td[(T)104(rial)-404(division)-404(is)-404(great)-405(fo)35(r)-404(\014nding)-404(small)-405(facto)34(rs.)]TJ 0 -57.79 Td[(The)-410(adversa)35(ry)-410(picks)]TJ/F19 19.83 Tf 209.94 0 Td[(N)]TJ/F15 19.83 Tf 26.98 0 Td[(with)-411(exactly)-410(t)34(w)35(o)-411(p)35(rime)]TJ -236.92 -27.89 Td[(diviso)35(rs,)-417(b)-34(oth)-418(la)35(rge.)]TJ 0 -57.78 Td[(What)-417(if)-417(w)34(e)-416(magically)-416(knew)-418(p)35(rime)-416(numb)-36(ers?)]TJ 0 -57.79 Td[(W)35(e)-416(w)34(ouldn't)-418(have)-416(to)-417(try)-417(9)-417(o)35(r)-416(77.)]TJ 0 -57.78 Td[(De\014nition.)]TJ/F19 19.83 Tf 116.79 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)-417(is)-417(the)-417(numb)-35(er)-416(of)-417(p)35(rimes)]TJ -151.1 -27.9 Td[(b)-35(et)35(w)34(een)-416(1)-417(and)]TJ/F19 19.83 Tf 156.32 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(.)]TJ -168.18 -57.78 Td[(No)35(w)-417(check)-416(only)]TJ/F19 19.83 Tf 167.61 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F22 19.83 Tf 9.64 16.68 Td[(p)]TJ ET 41.21 -385.81 18.84 0.89 re f 1 0 0 1 41.21 -402.49 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051)-417(things.)]TJ ET endstream endobj 39 0 obj 1262 endobj 36 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 37 0 obj << /Type /Page /Contents 38 0 R /Resources 36 0 R /MediaBox [0 0 595.27 841.89] /Parent 35 0 R >> endobj 42 0 obj << /Length 43 0 R >> stream 1 0 0 1 238.79 703.93 cm BT /F15 19.83 Tf 0 0 Td[(T)104(rial)-416(Division)]TJ -166.41 -57.78 Td[(De\014nition.)]TJ/F19 19.83 Tf 116.79 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)-417(is)-417(the)-417(numb)-35(er)-416(of)-417(p)35(rimes)]TJ -151.1 -27.89 Td[(b)-35(et)35(w)34(een)-416(1)-417(and)]TJ/F19 19.83 Tf 156.32 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(.)]TJ/F33 19.83 Tf -168.18 -57.79 Td[(Cheb)40(yshev's)-459(Theo)39(rem)]TJ/F19 19.83 Tf 252.63 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F19 19.83 Tf 15.5 0 Td[(>)-295(x=)]TJ/F15 19.83 Tf 44.64 0 Td[(2)-177(log)]TJ/F19 19.83 Tf 49.72 0 Td[(x:)]TJ/F33 19.83 Tf -396.8 -57.78 Td[(Prime)-304(Numb)-38(er)-305(Theo)39(rem)]TJ/F15 19.83 Tf 272.14 0 Td[(\0501896\051)]TJ/F19 19.83 Tf 74.38 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F22 19.83 Tf 15.5 0 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(x=)]TJ/F15 19.83 Tf 25.91 0 Td[(log)]TJ/F19 19.83 Tf 33.81 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(.)]TJ -490.15 -85.68 Td[(conjectured)-676(b)34(y)-677(Gauss,)-746(p)35(roved)-677(b)35(y)-678(Hadama)33(rd)]TJ 0 -27.89 Td[(and)-417(de)-416(la)-417(V)35(all)34()591(ee-P)36(oussin.)]TJ 0 -85.68 Td[(Conclusion.)]TJ/F19 19.83 Tf 127.26 0 Td[(O)]TJ/F15 19.83 Tf 16.57 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F22 19.83 Tf 9.64 16.67 Td[(p)]TJ ET 27.07 -383.82 18.84 0.89 re f 1 0 0 1 27.07 -400.49 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051\051)-417(is)-417(still)-417(slo)35(w.)]TJ -212.32 -57.79 Td[(F)35(un)-417(fact:)]TJ/F20 16.53 Tf 164.22 -25.15 Td[(p)]TJ/F17 16.53 Tf 17.1 0 Td[(p)35(rime)]TJ/F25 17.22 Tf 3.69 -6.85 Td[(Y)]TJ/F20 16.53 Tf -38.73 -40.17 Td[(s
> /ProcSet [/PDF /Text] >> endobj 41 0 obj << /Type /Page /Contents 42 0 R /Resources 40 0 R /MediaBox [0 0 595.27 841.89] /Parent 35 0 R >> endobj 48 0 obj << /Length 49 0 R >> stream 1 0 0 1 167.86 702.19 cm BT /F15 19.83 Tf 0 0 Td[(Summa)34(ry)-416(of)-417(F)35(ast)-418(and)-417(Slo)35(w)]TJ -95.48 -57.78 Td[(De\014nition.)]TJ/F19 19.83 Tf 116.79 0 Td[(L)]TJ/F20 16.53 Tf 14.33 -4.47 Td[(N)]TJ/F15 19.83 Tf 16.2 4.47 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-36(;)-177()]TJ/F15 19.83 Tf 32.63 0 Td[(])-417(is)]TJ/F19 19.83 Tf -117.65 -42.84 Td[(O)]TJ/F15 19.83 Tf 16.57 0 Td[(\050exp\050)]TJ/F19 19.83 Tf 53.72 0 Td[()]TJ/F15 19.83 Tf 12.29 0 Td[(\050log)]TJ/F19 19.83 Tf 43.45 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051)]TJ/F20 16.53 Tf 9.64 8.24 Td[(v)]TJ/F15 19.83 Tf 9.64 -8.24 Td[(\050log)-177(log)]TJ/F19 19.83 Tf 77.27 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(\051)]TJ/F17 16.53 Tf 9.64 8.24 Td[(1)]TJ/F23 16.53 Tf 10.33 0 Td[( )]TJ/F20 16.53 Tf 13.66 0 Td[(v)]TJ/F15 19.83 Tf 9.64 -8.24 Td[(\051\051)]TJ/F19 19.83 Tf 19.29 0 Td[(:)]TJ -392.1 -67.75 Td[(L)]TJ/F20 16.53 Tf 14.33 -4.46 Td[(N)]TJ/F15 19.83 Tf 16.19 4.46 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)]TJ/F15 19.83 Tf 10.98 0 Td[(])-417(includes)]TJ/F19 19.83 Tf 103.26 0 Td[(L)]TJ/F20 16.53 Tf 14.33 -4.46 Td[(N)]TJ/F15 19.83 Tf 16.19 4.46 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-36(;)-178()]TJ/F15 19.83 Tf 32.63 0 Td[(])-417(fo)34(r)-416(every)]TJ/F19 19.83 Tf 111.66 0 Td[()]TJ/F15 19.83 Tf 12.3 0 Td[(.)]TJ/F19 19.83 Tf -345.85 -57.78 Td[(L)]TJ/F20 16.53 Tf 14.33 -4.46 Td[(N)]TJ/F15 19.83 Tf 16.19 4.46 Td[([1])-418(is)-417(slo)35(w.)-556(e.g.)-556(trial)-417(division.)]TJ/F19 19.83 Tf -30.52 -57.78 Td[(L)]TJ/F20 16.53 Tf 14.33 -4.47 Td[(N)]TJ/F15 19.83 Tf 16.19 4.47 Td[([0])-418(is)-417(fast,)-418(e.g.)]TJ/F19 19.83 Tf 159.01 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.71 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(N)-48(;)-177(a)]TJ/F15 19.83 Tf 38.23 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -297.75 -85.68 Td[(Avoid)-416(emba)35(rrassment!)]TJ 0 -27.9 Td[(Check)-416(whether)]TJ/F19 19.83 Tf 159.07 0 Td[(N)]TJ/F15 19.83 Tf 27.1 0 Td[(is)-417(comp)-35(osite.)]TJ -186.17 -57.78 Td[(Answ)35(ering)-417(\134Is)]TJ/F19 19.83 Tf 148.05 0 Td[(N)]TJ/F15 19.83 Tf 27.1 0 Td[(comp)-35(osite?")-556(is)]TJ/F19 19.83 Tf 161.56 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([0].)]TJ -351.04 -27.9 Td[(New)-416(result)-417(in)-416('02.)-557(Previous)-416(b)-34(est)-417(w)34(as)]TJ/F19 19.83 Tf 121.17 -42.84 Td[(O)]TJ/F15 19.83 Tf 16.57 0 Td[(\050\050log)]TJ/F19 19.83 Tf 53.09 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051)]TJ/F20 16.53 Tf 9.64 8.24 Td[(c)]TJ/F17 16.53 Tf 10.54 0 Td[(log)-176(log)-177(log)]TJ/F20 16.53 Tf 84.53 0 Td[(N)]TJ/F15 19.83 Tf 16.2 -8.24 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ ET endstream endobj 49 0 obj 2580 endobj 46 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F20 12 0 R /F17 5 0 R /F23 13 0 R >> /ProcSet [/PDF /Text] >> endobj 47 0 obj << /Type /Page /Contents 48 0 R /Resources 46 0 R /MediaBox [0 0 595.27 841.89] /Parent 35 0 R >> endobj 52 0 obj << /Length 53 0 R >> stream 1 0 0 1 207.04 663.28 cm BT /F15 19.83 Tf 0 0 Td[(Analytical)-416(Estimate)]TJ -134.66 -57.78 Td[(Let)-417(\011\050)]TJ/F19 19.83 Tf 71.2 0 Td[(x;)-177(y)]TJ/F15 19.83 Tf 32.35 0 Td[(\051)]TJ -103.55 -27.9 Td[(b)-35(e)-416(numb)-35(er)-416(of)-417(integers)-417(b)-34(et)34(w)35(een)-416(1)-417(and)]TJ/F19 19.83 Tf 388.94 0 Td[(x)]TJ/F15 19.83 Tf -388.94 -27.89 Td[(with)-417(all)-417(p)35(rime)-417(diviso)35(rs)-416(less)-417(than)]TJ/F19 19.83 Tf 325.86 0 Td[(y)]TJ/F15 19.83 Tf 11.12 0 Td[(.)]TJ/F33 19.83 Tf -336.98 -57.79 Td[(Theo)40(rem)]TJ/F15 19.83 Tf 109.08 0 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(u)]TJ/F15 19.83 Tf 20.46 0 Td[(suciently)-416(la)34(rge)-416(and)]TJ/F19 19.83 Tf 216.78 0 Td[(x)-296(>)]TJ/F15 19.83 Tf 39.96 0 Td[(1,)]TJ -323.94 -42.84 Td[(\011\050)]TJ/F19 19.83 Tf 28.92 0 Td[(x;)-178(x)]TJ/F17 16.53 Tf 33.09 8.24 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.45 -8.24 Td[(\051)]TJ/F19 19.83 Tf 15.49 0 Td[(>)-295(x=u)]TJ/F20 16.53 Tf 56.84 8.24 Td[(u)]TJ/F17 16.53 Tf 10.17 0 Td[(\0501+)]TJ/F20 16.53 Tf 34.43 0 Td[(o)]TJ/F17 16.53 Tf 8.49 0 Td[(\0501\051\051)]TJ/F19 19.83 Tf 34.93 -8.24 Td[(:)]TJ/F33 19.83 Tf -356.76 -67.74 Td[(Lemma)-457(\050Can\014eld-Erd})689(os-P)39(omerance\051)]TJ/F15 19.83 Tf 0 -27.9 Td[(There)-416(is)-416(a)-417(constant)]TJ/F19 19.83 Tf 207.55 0 Td[(c)]TJ/F15 19.83 Tf 17.39 0 Td[(such)-417(that)]TJ -224.94 -27.89 Td[(fo)35(r)]TJ/F19 19.83 Tf 35.8 0 Td[(u)-296(>)-294(c)]TJ/F15 19.83 Tf 57.69 0 Td[(and)-417(all)]TJ/F19 19.83 Tf 75.75 0 Td[(x)-295(>)]TJ/F15 19.83 Tf 39.96 0 Td[(1,)]TJ -209.2 -27.9 Td[(if)]TJ/F19 19.83 Tf 21.34 0 Td[(u)-296(>)]TJ/F15 19.83 Tf 40.3 0 Td[(\050log)]TJ/F19 19.83 Tf 43.45 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F17 16.53 Tf 9.65 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(=)]TJ/F17 16.53 Tf 8.78 0 Td[(8)]TJ/F19 19.83 Tf 10.82 -7 Td[(;)]TJ/F15 19.83 Tf 14.12 0 Td[(then)]TJ -32.52 -42.84 Td[(\011\050)]TJ/F19 19.83 Tf 28.93 0 Td[(x;)-177(x)]TJ/F17 16.53 Tf 33.08 8.24 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.45 -8.24 Td[(\051)]TJ/F19 19.83 Tf 15.49 0 Td[(>)-295(x=u)]TJ/F17 16.53 Tf 56.85 8.24 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F19 19.83 Tf 10.66 -8.24 Td[(:)]TJ ET endstream endobj 53 0 obj 2206 endobj 50 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F33 44 0 R /F17 5 0 R /F20 12 0 R >> /ProcSet [/PDF /Text] >> endobj 51 0 obj << /Type /Page /Contents 52 0 R /Resources 50 0 R /MediaBox [0 0 595.27 841.89] /Parent 35 0 R >> endobj 56 0 obj << /Length 57 0 R >> stream 1 0 0 1 207.04 684.59 cm BT /F15 19.83 Tf 0 0 Td[(Analytical)-416(Estimate)]TJ/F33 19.83 Tf -134.66 -57.78 Td[(Lemma)-457(\050Can\014eld-Erd})689(os-P)39(omerance\051)]TJ/F15 19.83 Tf 0 -27.9 Td[(There)-416(is)-416(a)-417(constant)]TJ/F19 19.83 Tf 207.55 0 Td[(c)]TJ/F15 19.83 Tf 17.39 0 Td[(such)-417(that)]TJ -224.94 -27.89 Td[(fo)35(r)]TJ/F19 19.83 Tf 35.8 0 Td[(u)-296(>)-294(c)]TJ/F15 19.83 Tf 57.69 0 Td[(and)-417(all)]TJ/F19 19.83 Tf 75.75 0 Td[(x)-295(>)]TJ/F15 19.83 Tf 39.96 0 Td[(1,)]TJ -209.2 -27.9 Td[(if)]TJ/F19 19.83 Tf 21.34 0 Td[(u)-296(>)]TJ/F15 19.83 Tf 40.3 0 Td[(\050log)]TJ/F19 19.83 Tf 43.45 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F17 16.53 Tf 9.65 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(=)]TJ/F17 16.53 Tf 8.78 0 Td[(8)]TJ/F19 19.83 Tf 10.82 -7 Td[(;)]TJ/F15 19.83 Tf 14.12 0 Td[(then)]TJ -32.52 -42.84 Td[(\011\050)]TJ/F19 19.83 Tf 28.93 0 Td[(x;)-177(x)]TJ/F17 16.53 Tf 33.08 8.24 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.45 -8.24 Td[(\051)]TJ/F19 19.83 Tf 15.49 0 Td[(>)-295(x=u)]TJ/F17 16.53 Tf 56.85 8.24 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F19 19.83 Tf 10.66 -8.24 Td[(:)]TJ/F15 19.83 Tf -323.25 -67.74 Td[(Pro)-34(of.)-556(If)]TJ/F19 19.83 Tf 96.96 0 Td[(x)-295(<)-295(u)]TJ/F17 16.53 Tf 52.15 6.99 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F15 19.83 Tf 10.67 -6.99 Td[(,)-417(trivial.)]TJ -170.11 -57.79 Td[(Supp)-34(ose)]TJ/F19 19.83 Tf 92.82 0 Td[(x)]TJ/F22 19.83 Tf 17.72 0 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(u)]TJ/F17 16.53 Tf 12.2 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F22 19.83 Tf 16.52 -7 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(c)]TJ/F17 16.53 Tf 9.13 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(c)]TJ/F22 19.83 Tf 13.96 -7 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(c)]TJ/F17 16.53 Tf 9.13 7 Td[(3)]TJ/F19 19.83 Tf 10.83 -7 Td[(:)]TJ/F15 19.83 Tf -269.69 -57.78 Td[(By)-416(Cheb)36(yshev,)]TJ/F19 19.83 Tf 156.59 0 Td[()]TJ/F15 19.83 Tf 12.81 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F17 16.53 Tf 11.87 7 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.44 -7 Td[(\051)]TJ/F19 19.83 Tf 15.5 0 Td[(>)-294(ux)]TJ/F17 16.53 Tf 46.3 7 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F19 19.83 Tf 19.45 -7 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(2)-177(log)]TJ/F19 19.83 Tf 49.72 0 Td[(x:)]TJ/F15 19.83 Tf -372.51 -57.78 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[(m)]TJ/F15 19.83 Tf 24.49 0 Td[(=)]TJ/F22 19.83 Tf 25.14 0 Td[(b)]TJ/F19 19.83 Tf 9.36 0 Td[(u)]TJ/F22 19.83 Tf 12.2 0 Td[(c)]TJ/F15 19.83 Tf 9.37 0 Td[(;)]TJ/F19 19.83 Tf 15.15 0 Td[(u)]TJ/F15 19.83 Tf 18.05 0 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(m)]TJ/F15 19.83 Tf 23.32 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[()]TJ/F15 19.83 Tf 10.42 0 Td[(.)]TJ -238.88 -57.79 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[()]TJ/F23 16.53 Tf 12.81 7 Td[(0)]TJ/F15 19.83 Tf 5.26 -7 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(y)]TJ/F15 19.83 Tf 11.13 0 Td[(\051)-295(=)-296(max\0501)]TJ/F19 19.83 Tf 104.67 0 Td[(;)-177()]TJ/F15 19.83 Tf 22.18 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(y)]TJ/F15 19.83 Tf 11.13 0 Td[(\051\051.)]TJ ET endstream endobj 57 0 obj 3005 endobj 54 0 obj << /Font << /F15 5 0 R /F33 44 0 R /F19 12 0 R /F17 5 0 R /F20 12 0 R /F22 13 0 R /F23 13 0 R >> /ProcSet [/PDF /Text] >> endobj 55 0 obj << /Type /Page /Contents 56 0 R /Resources 54 0 R /MediaBox [0 0 595.27 841.89] /Parent 35 0 R >> endobj 60 0 obj << /Length 61 0 R >> stream 1 0 0 1 207.04 681.27 cm BT /F15 19.83 Tf 0 0 Td[(Analytical)-416(Estimate)]TJ/F33 19.83 Tf -134.66 -57.78 Td[(Lemma)-457(\050Can\014eld-Erd})689(os-P)39(omerance\051)]TJ/F15 19.83 Tf 0 -27.9 Td[(There)-416(is)-416(a)-417(constant)]TJ/F19 19.83 Tf 207.55 0 Td[(c)]TJ/F15 19.83 Tf 17.39 0 Td[(such)-417(that)]TJ -224.94 -27.89 Td[(fo)35(r)]TJ/F19 19.83 Tf 35.8 0 Td[(u)-296(>)-294(c)]TJ/F15 19.83 Tf 57.69 0 Td[(and)-417(all)]TJ/F19 19.83 Tf 75.75 0 Td[(x)-295(>)]TJ/F15 19.83 Tf 39.96 0 Td[(1,)]TJ -209.2 -27.9 Td[(if)]TJ/F19 19.83 Tf 21.34 0 Td[(u)-296(>)]TJ/F15 19.83 Tf 40.3 0 Td[(\050log)]TJ/F19 19.83 Tf 43.45 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F17 16.53 Tf 9.65 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(=)]TJ/F17 16.53 Tf 8.78 0 Td[(8)]TJ/F19 19.83 Tf 10.82 -7 Td[(;)]TJ/F15 19.83 Tf 14.12 0 Td[(then)]TJ -32.52 -42.84 Td[(\011\050)]TJ/F19 19.83 Tf 28.93 0 Td[(x;)-177(x)]TJ/F17 16.53 Tf 33.08 8.24 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.45 -8.24 Td[(\051)]TJ/F19 19.83 Tf 15.49 0 Td[(>)-295(x=u)]TJ/F17 16.53 Tf 56.85 8.24 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F19 19.83 Tf 10.66 -8.24 Td[(:)]TJ/F15 19.83 Tf -323.25 -67.75 Td[(Pro)-34(of)-417(\050continued\051.)]TJ 0 -57.78 Td[(Claim.)-556(\0502)-177(log)]TJ/F19 19.83 Tf 135.11 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F20 16.53 Tf 9.64 7 Td[(m)]TJ/F17 16.53 Tf 15.53 0 Td[(+1)]TJ/F19 19.83 Tf 32.75 -7 Td[(<)-295(u)]TJ/F17 16.53 Tf 34.45 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F15 19.83 Tf 16.51 -7 Td[(:)]TJ -170.15 -42.84 Td[(\0502)-178(log)]TJ/F19 19.83 Tf 59.36 0 Td[(x)]TJ/F15 19.83 Tf 11.87 0 Td[(\051)]TJ/F20 16.53 Tf 9.64 8.24 Td[(m)]TJ/F17 16.53 Tf 15.53 0 Td[(+1)]TJ/F19 19.83 Tf 32.75 -8.24 Td[(<)]TJ/F15 19.83 Tf 22.24 0 Td[(\0502)-178(log)]TJ/F19 19.83 Tf 59.36 0 Td[(x)]TJ/F15 19.83 Tf 11.87 0 Td[(\051)]TJ/F20 16.53 Tf 9.64 8.24 Td[(u)]TJ/F17 16.53 Tf 10.16 0 Td[(+1)]TJ/F19 19.83 Tf 26.9 -8.24 Td[(:)]TJ/F15 19.83 Tf -365.35 -67.74 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(u)-295(>)]TJ/F15 19.83 Tf 40.29 0 Td[(3)-417(and)]TJ/F19 19.83 Tf 65.42 0 Td[(u)]TJ/F22 19.83 Tf 18.06 0 Td[()]TJ/F15 19.83 Tf 22.24 0 Td[(log)]TJ/F17 16.53 Tf 30.3 7.23 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(=)]TJ/F17 16.53 Tf 8.78 0 Td[(8)]TJ/F19 19.83 Tf 14.34 -7.23 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(,)]TJ -132.71 -42.84 Td[(\0502)-177(log)]TJ/F19 19.83 Tf 59.36 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F20 16.53 Tf 9.65 8.24 Td[(u)]TJ/F17 16.53 Tf 10.16 0 Td[(+1)]TJ/F22 19.83 Tf 32.75 -8.24 Td[()]TJ/F15 19.83 Tf 22.25 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(u)]TJ/F17 16.53 Tf 12.2 8.24 Td[(3)]TJ/F15 19.83 Tf 10.83 -8.24 Td[(\051)]TJ/F20 16.53 Tf 9.64 8.24 Td[(u)]TJ/F19 19.83 Tf 10.66 -8.24 Td[(:)]TJ ET endstream endobj 61 0 obj 2709 endobj 58 0 obj << /Font << /F15 5 0 R /F33 44 0 R /F19 12 0 R /F17 5 0 R /F20 12 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 59 0 obj << /Type /Page /Contents 60 0 R /Resources 58 0 R /MediaBox [0 0 595.27 841.89] /Parent 62 0 R >> endobj 65 0 obj << /Length 66 0 R >> stream 1 0 0 1 207.04 703.69 cm BT /F15 19.83 Tf 0 0 Td[(Analytical)-416(Estimate)]TJ/F33 19.83 Tf -134.66 -57.79 Td[(Lemma)-457(\050Can\014eld-Erd})689(os-P)39(omerance\051)]TJ/F15 19.83 Tf 0 -27.89 Td[(There)-416(is)-416(a)-417(constant)]TJ/F19 19.83 Tf 207.55 0 Td[(c)]TJ/F15 19.83 Tf 17.39 0 Td[(such)-417(that)]TJ -224.94 -27.9 Td[(fo)35(r)]TJ/F19 19.83 Tf 35.8 0 Td[(u)-296(>)-294(c)]TJ/F15 19.83 Tf 57.69 0 Td[(and)-417(all)]TJ/F19 19.83 Tf 75.75 0 Td[(x)-295(>)]TJ/F15 19.83 Tf 39.96 0 Td[(1,)]TJ -209.2 -27.89 Td[(if)]TJ/F19 19.83 Tf 21.34 0 Td[(u)-296(>)]TJ/F15 19.83 Tf 40.3 0 Td[(\050log)]TJ/F19 19.83 Tf 43.45 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F17 16.53 Tf 9.65 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(=)]TJ/F17 16.53 Tf 8.78 0 Td[(8)]TJ/F19 19.83 Tf 10.82 -7 Td[(;)]TJ/F15 19.83 Tf 14.12 0 Td[(then)]TJ -32.52 -42.84 Td[(\011\050)]TJ/F19 19.83 Tf 28.93 0 Td[(x;)-177(x)]TJ/F17 16.53 Tf 33.08 8.24 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.45 -8.24 Td[(\051)]TJ/F19 19.83 Tf 15.49 0 Td[(>)-295(x=u)]TJ/F17 16.53 Tf 56.85 8.24 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F19 19.83 Tf 10.66 -8.24 Td[(:)]TJ/F15 19.83 Tf -323.25 -67.75 Td[(Pro)-34(of)-417(\050concluded\051.)]TJ 26.95 -40.46 Td[(\011\050)]TJ/F19 19.83 Tf 28.93 0 Td[(x;)-177(x)]TJ/F17 16.53 Tf 33.09 7 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.44 -7 Td[(\051)]TJ/F19 19.83 Tf 25.58 0 Td[(>)-804()]TJ/F15 19.83 Tf 45.15 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F17 16.53 Tf 11.86 7 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=u)]TJ/F15 19.83 Tf 19.44 -7 Td[(\051)]TJ/F20 16.53 Tf 9.64 7 Td[(m)]TJ/F19 19.83 Tf 16.04 -7 Td[()]TJ/F23 16.53 Tf 12.81 7 Td[(0)]TJ/F15 19.83 Tf 5.26 -7 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F20 16.53 Tf 11.86 7 Td[()-29(=u)]TJ/F15 19.83 Tf 28.13 -7 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(m)]TJ/F15 19.83 Tf 23.32 0 Td[(+)-236(1\051!)]TJ/F19 19.83 Tf -242.94 -56.48 Td[(>)]TJ/F17 16.53 Tf 34.78 9.44 Td[(\050)]TJ/F20 16.53 Tf 8.04 0 Td[(ux)]TJ/F18 13.77 Tf 20.05 5.83 Td[(1)]TJ/F21 13.77 Tf 8.61 0 Td[(=u)]TJ/F17 16.53 Tf 16.28 -5.83 Td[(\051)]TJ/F21 13.77 Tf 8.03 5.83 Td[(m)]TJ/F20 16.53 Tf 13.44 -5.83 Td[(x)]TJ/F21 13.77 Tf 9.89 5.83 Td[()-29(=u)]TJ ET 43.19 -344.38 110.35 0.69 re f 1 0 0 1 43.19 -360.66 cm BT /F17 16.53 Tf 0 0 Td[(2)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F21 13.77 Tf 10.17 4.71 Td[(m)]TJ/F17 16.53 Tf 16.36 -4.71 Td[(log)]TJ/F21 13.77 Tf 25.25 6.03 Td[(m)]TJ/F18 13.77 Tf 12.94 0 Td[(+1)]TJ/F20 16.53 Tf 25.42 -6.03 Td[(x)]TJ/F15 19.83 Tf -101.67 -44.68 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(x=)]TJ/F15 19.83 Tf 22.4 0 Td[(\0502)-177(log)]TJ/F19 19.83 Tf 59.36 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(\051)]TJ/F20 16.53 Tf 9.64 7 Td[(m)]TJ/F17 16.53 Tf 15.53 0 Td[(+1)]TJ/F19 19.83 Tf -176.26 -55.79 Td[(>)-804(x=u)]TJ/F17 16.53 Tf 66.93 7 Td[(3)]TJ/F20 16.53 Tf 10.33 0 Td[(u)]TJ/F19 19.83 Tf 10.67 -7 Td[(:)]TJ/F15 19.83 Tf -232.25 -62.59 Td[(Exeunt)-416(Can\014eld,)-417(Erd})626(os,)-418(and)-417(P)35(omerance.)]TJ 0 -27.9 Td[(Enter)-416(F)34(ermat.)]TJ ET endstream endobj 66 0 obj 3078 endobj 63 0 obj << /Font << /F15 5 0 R /F33 44 0 R /F19 12 0 R /F17 5 0 R /F20 12 0 R /F23 13 0 R /F18 5 0 R /F21 12 0 R >> /ProcSet [/PDF /Text] >> endobj 64 0 obj << /Type /Page /Contents 65 0 R /Resources 63 0 R /MediaBox [0 0 595.27 841.89] /Parent 62 0 R >> endobj 69 0 obj << /Length 70 0 R >> stream 1 0 0 1 217.99 673.25 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ermat's)-417(Metho)-35(d)]TJ -145.61 -57.78 Td[(Quick...)-557(facto)35(r)-417(3599.)]TJ 0 -113.58 Td[(3599)-295(=)-296(60)]TJ/F17 16.53 Tf 105.36 7 Td[(2)]TJ/F22 19.83 Tf 15.51 -7 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)]TJ/F17 16.53 Tf 12.4 7 Td[(2)]TJ/F15 19.83 Tf 10.82 -7 Td[(.)]TJ -165.16 -113.57 Td[(If)]TJ/F19 19.83 Tf 22.17 0 Td[(x)]TJ/F17 16.53 Tf 11.86 7 Td[(2)]TJ/F22 19.83 Tf 16.68 -7 Td[()]TJ/F19 19.83 Tf 22.25 0 Td[(y)]TJ/F17 16.53 Tf 11.12 7 Td[(2)]TJ/F15 19.83 Tf 19.1 -7 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(\051,)-417(compute)]TJ/F19 19.83 Tf 120.51 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.72 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F22 19.83 Tf 16.54 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(y)-36(;)-178(N)]TJ/F15 19.83 Tf 39.34 0 Td[(\051.)]TJ -389.47 -57.78 Td[(50%)-416(chance)-417(to)-417(get)-417(a)-417(facto)34(r)-416(of)]TJ/F19 19.83 Tf 317.46 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(,)-417(b)-35(ecause)]TJ -218.51 -42.84 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F22 19.83 Tf 16.55 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(y)]TJ/F15 19.83 Tf 11.13 0 Td[(\051\050)]TJ/F19 19.83 Tf 19.28 0 Td[(x)]TJ/F15 19.83 Tf 16.54 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(y)]TJ/F15 19.83 Tf 11.13 0 Td[(\051)]TJ/F22 19.83 Tf 15.49 0 Td[()]TJ/F15 19.83 Tf 22.24 0 Td[(0)-417(\050)]TJ/F19 19.83 Tf 30.3 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -343.6 -67.75 Td[(3599)-295(=)-296(59)]TJ/F22 19.83 Tf 110.04 0 Td[()]TJ/F15 19.83 Tf 10.54 0 Td[(61)]TJ/F19 19.83 Tf 24.79 0 Td[(:)]TJ ET endstream endobj 70 0 obj 1618 endobj 67 0 obj << /Font << /F15 5 0 R /F17 5 0 R /F22 13 0 R /F19 12 0 R >> /ProcSet [/PDF /Text] >> endobj 68 0 obj << /Type /Page /Contents 69 0 R /Resources 67 0 R /MediaBox [0 0 595.27 841.89] /Parent 62 0 R >> endobj 73 0 obj << /Length 74 0 R >> stream 1 0 0 1 217.99 646.35 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ermat's)-417(Metho)-35(d)]TJ -145.61 -57.78 Td[(F)35(ermat's)-418(metho)-35(d:)-556(fo)34(r)-416(each)]TJ/F19 19.83 Tf 283.16 0 Td[(x)]TJ/F15 19.83 Tf 17.72 0 Td[(=)-295(1)]TJ/F19 19.83 Tf 37.53 0 Td[(;)]TJ/F15 19.83 Tf 9.36 0 Td[(2)]TJ/F19 19.83 Tf 12.4 0 Td[(;)-177(:::)]TJ/F15 19.83 Tf 26.92 0 Td[(,)]TJ -387.09 -27.9 Td[(check)-416(whether)]TJ/F19 19.83 Tf 154.25 0 Td[(N)]TJ/F15 19.83 Tf 23.52 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(x)]TJ/F17 16.53 Tf 11.87 7 Td[(2)]TJ/F15 19.83 Tf 19.09 -7 Td[(is)-417(a)-417(squa)34(re.)]TJ -232.69 -57.78 Td[(The)-416(adversa)35(ry)-417(cho)-34(oses)]TJ/F19 19.83 Tf 239.09 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(pq)]TJ/F15 19.83 Tf 28.99 0 Td[(with)]TJ -317.91 -27.9 Td[(p)35(rime)-416(facto)34(rs)-417(fa)35(r)-417(a)34(w)35(a)34(y)-416(from)]TJ/F22 19.83 Tf 289.08 16.68 Td[(p)]TJ ET 161.03 -154.68 18.84 0.89 re f 1 0 0 1 161.03 -171.36 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(.)]TJ/F19 19.83 Tf -325.48 -57.78 Td[(p)]TJ/F22 19.83 Tf 16.46 0 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(N)]TJ/F17 16.53 Tf 18.84 7 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=e)]TJ/F15 19.83 Tf 25.69 -7 Td[(will)-416(do.)]TJ -93.56 -57.78 Td[(No)35(w,)-734(F)35(ermat's)-671(metho)-35(d)-670(is)]TJ/F19 19.83 Tf 287.42 0 Td[(O)]TJ/F15 19.83 Tf 16.58 0 Td[(\050)]TJ/F22 19.83 Tf 9.64 16.67 Td[(p)]TJ ET 24.56 -98.89 18.84 0.89 re f 1 0 0 1 24.56 -115.56 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(\051,)-734(which)-670(is)]TJ -350.03 -27.9 Td[(slo)35(w.)]TJ 0 -57.78 Td[(Let's)-418(use)-416(another)-417(idea)-417(of)-417(F)35(ermat.)]TJ ET endstream endobj 74 0 obj 1668 endobj 71 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F17 5 0 R /F22 13 0 R /F20 12 0 R >> /ProcSet [/PDF /Text] >> endobj 72 0 obj << /Type /Page /Contents 73 0 R /Resources 71 0 R /MediaBox [0 0 595.27 841.89] /Parent 62 0 R >> endobj 77 0 obj << /Length 78 0 R >> stream 1 0 0 1 217.99 628.01 cm BT /F15 19.83 Tf 0 0 Td[(F)34(ermat's)-417(Metho)-35(d)]TJ -145.61 -57.79 Td[(\050This)-417(isn't)-417(the)-417(other)-417(useful)-416(F)34(ermat)-417(idea.\051)]TJ 0 -85.67 Td[(F)35(acto)34(r)-416(64027.)]TJ 0 -113.58 Td[(Y)105(es,)]TJ/F19 19.83 Tf 49.58 0 Td[(x)]TJ/F17 16.53 Tf 11.86 7 Td[(3)]TJ/F15 19.83 Tf 15.51 -7 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(y)]TJ/F17 16.53 Tf 11.13 7 Td[(3)]TJ/F15 19.83 Tf 16.68 -7 Td[(=)-296(\050)]TJ/F19 19.83 Tf 34.78 0 Td[(x)]TJ/F15 19.83 Tf 16.54 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(y)]TJ/F15 19.83 Tf 11.13 0 Td[(\051\050)]TJ/F19 19.83 Tf 19.28 0 Td[(x)]TJ/F17 16.53 Tf 11.86 7 Td[(2)]TJ/F22 19.83 Tf 15.51 -7 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(xy)]TJ/F15 19.83 Tf 27.67 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(y)]TJ/F17 16.53 Tf 11.13 7 Td[(2)]TJ/F15 19.83 Tf 10.82 -7 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -366.09 -57.78 Td[(But)-417(cub)-34(es)-417(a)35(re)-416(ra)34(rer)-416(than)-417(squa)34(res.)]TJ ET endstream endobj 78 0 obj 990 endobj 75 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F17 5 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 76 0 obj << /Type /Page /Contents 77 0 R /Resources 75 0 R /MediaBox [0 0 595.27 841.89] /Parent 62 0 R >> endobj 81 0 obj << /Length 82 0 R >> stream 1 0 0 1 191.13 681.27 cm BT /F15 19.83 Tf 0 0 Td[(P)35(olla)34(rd's)]TJ/F19 19.83 Tf 94.62 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)-417(Metho)-35(d)]TJ/F33 19.83 Tf -249.73 -57.78 Td[(F)38(ermat's)-457(Little)-457(Theo)40(rem)]TJ/F15 19.83 Tf 0 -27.9 Td[(If)]TJ/F19 19.83 Tf 24.62 0 Td[(p)]TJ/F15 19.83 Tf 21.32 0 Td[(is)-540(p)35(rime)-540(and)]TJ/F19 19.83 Tf 139.42 0 Td[(a)]TJ/F22 19.83 Tf 20.52 0 Td[(2)]TJ/F34 20.66 Tf 23.37 0 Td[(Z)]TJ/F15 19.83 Tf 14.2 0 Td[(,)-572(and)]TJ/F19 19.83 Tf 65.42 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.72 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(a;)-178(p)]TJ/F15 19.83 Tf 31.16 0 Td[(\051)-470(=)-471(1,)]TJ -400.39 -27.89 Td[(then)]TJ/F19 19.83 Tf 169.11 -37.86 Td[(a)]TJ/F20 16.53 Tf 11.19 8.24 Td[(p)]TJ/F23 16.53 Tf 8.84 0 Td[( )]TJ/F17 16.53 Tf 13.66 0 Td[(1)]TJ/F22 19.83 Tf 16.68 -8.24 Td[()]TJ/F15 19.83 Tf 22.25 0 Td[(1)-417(\050)]TJ/F19 19.83 Tf 30.3 0 Td[(p)]TJ/F15 19.83 Tf 10.6 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -292.27 -67.75 Td[(Given)]TJ/F19 19.83 Tf 63.87 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(,)-382(if)-373(a)-374(kind)-374(o)35(racle)-373(w)34(ould)-373(tell)-373(us)]TJ/F19 19.83 Tf 303.74 0 Td[(p)]TJ/F22 19.83 Tf 13.83 0 Td[( )]TJ/F15 19.83 Tf 19.62 0 Td[(1)-373(fo)34(r)]TJ/F19 19.83 Tf -419.9 -27.89 Td[(p)]TJ/F15 19.83 Tf 18.87 0 Td[(dividing)]TJ/F19 19.83 Tf 85.39 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(,)-417(then)]TJ/F19 19.83 Tf 26.93 -42.84 Td[(a)]TJ/F20 16.53 Tf 11.2 8.24 Td[(p)]TJ/F23 16.53 Tf 8.84 0 Td[( )]TJ/F17 16.53 Tf 13.66 0 Td[(1)]TJ/F22 19.83 Tf 15.51 -8.24 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)]TJ/F22 19.83 Tf 18.25 0 Td[()]TJ/F15 19.83 Tf 22.24 0 Td[(0)-417(\050)]TJ/F19 19.83 Tf 30.3 0 Td[(p)]TJ/F15 19.83 Tf 10.61 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -311.35 -67.75 Td[(Therefo)36(re,)]TJ/F19 19.83 Tf 114.17 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.71 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(a)]TJ/F20 16.53 Tf 11.2 7 Td[(p)]TJ/F23 16.53 Tf 8.84 0 Td[( )]TJ/F17 16.53 Tf 13.66 0 Td[(1)]TJ/F22 19.83 Tf 15.51 -7 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)]TJ/F19 19.83 Tf 12.39 0 Td[(;)-178(N)]TJ/F15 19.83 Tf 28.21 0 Td[(\051)-417(is)]TJ/F19 19.83 Tf 41.18 0 Td[(p)]TJ/F15 19.83 Tf 18.87 0 Td[(o)35(r)]TJ/F19 19.83 Tf 28.23 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(.)]TJ -392.52 -57.78 Td[(P)35(olla)35(rd's)-362(metho)-35(d)-362(\014nds)]TJ/F19 19.83 Tf 232.37 0 Td[(m)]TJ/F15 19.83 Tf 25.81 0 Td[(such)-361(that)-363(\050)]TJ/F19 19.83 Tf 111.3 0 Td[(p)]TJ/F22 19.83 Tf 13.43 0 Td[( )]TJ/F15 19.83 Tf 19.21 0 Td[(1\051)]TJ/F22 19.83 Tf 27.89 0 Td[(j)]TJ/F19 19.83 Tf 11.71 0 Td[(m)]TJ/F15 19.83 Tf 18.64 0 Td[(.)]TJ -460.36 -57.78 Td[(Thus,)]TJ/F19 19.83 Tf 67.21 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.71 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(a)]TJ/F20 16.53 Tf 11.19 6.99 Td[(m)]TJ/F22 19.83 Tf 20.72 -6.99 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)]TJ/F19 19.83 Tf 12.39 0 Td[(;)-178(N)]TJ/F15 19.83 Tf 28.21 0 Td[(\051)-417(is)]TJ/F19 19.83 Tf 41.18 0 Td[(p)]TJ/F15 19.83 Tf 18.87 0 Td[(o)35(r)]TJ/F19 19.83 Tf 28.23 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(.)]TJ ET endstream endobj 82 0 obj 3101 endobj 79 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F33 44 0 R /F34 83 0 R /F20 12 0 R /F23 13 0 R /F17 5 0 R >> /ProcSet [/PDF /Text] >> endobj 80 0 obj << /Type /Page /Contents 81 0 R /Resources 79 0 R /MediaBox [0 0 595.27 841.89] /Parent 62 0 R >> endobj 86 0 obj << /Length 87 0 R >> stream 1 0 0 1 191.13 628.67 cm BT /F15 19.83 Tf 0 0 Td[(P)35(olla)34(rd's)]TJ/F19 19.83 Tf 94.62 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)-417(Metho)-35(d)]TJ -249.73 -57.78 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[(m)]TJ/F20 16.53 Tf 18.64 -4.1 Td[(j)]TJ/F15 19.83 Tf 14.4 4.1 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(LC)-71(M)]TJ/F15 19.83 Tf 53.1 0 Td[(\0501)]TJ/F19 19.83 Tf 22.03 0 Td[(;)]TJ/F15 19.83 Tf 9.37 0 Td[(2)]TJ/F19 19.83 Tf 12.4 0 Td[(;)-177(:)-177(:)-178(:)-177(;)-177(j)]TJ/F15 19.83 Tf 56.49 0 Td[(\051.)]TJ -253.85 -57.78 Td[(Given)]TJ/F19 19.83 Tf 64.14 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)]TJ/F19 19.83 Tf 25.13 0 Td[(pq)]TJ/F15 19.83 Tf 20.73 0 Td[(,)-393(fo)35(r)-387(la)34(rge)-386(enough)]TJ/F19 19.83 Tf 186.44 0 Td[(j)]TJ/F15 19.83 Tf 9.66 0 Td[(,)]TJ/F19 19.83 Tf 14.68 0 Td[(p)]TJ/F22 19.83 Tf 14.29 0 Td[( )]TJ/F15 19.83 Tf 20.07 0 Td[(1)-387(divides)]TJ/F19 19.83 Tf -379.83 -27.9 Td[(m)]TJ/F20 16.53 Tf 18.64 -4.09 Td[(j)]TJ/F15 19.83 Tf 8.55 4.09 Td[(.)]TJ -27.19 -57.78 Td[(So:)]TJ/F19 19.83 Tf 44.07 0 Td[(a)]TJ/F20 16.53 Tf 11.19 8.22 Td[(m)]TJ/F21 13.77 Tf 15.53 -3.41 Td[(j)]TJ/F22 19.83 Tf 13.56 -4.81 Td[()]TJ/F15 19.83 Tf 22.25 0 Td[(1)-417(\050)]TJ/F19 19.83 Tf 30.3 0 Td[(p)]TJ/F15 19.83 Tf 10.6 0 Td[(\051.)-556(Ma)34(yb)-34(e)]TJ/F19 19.83 Tf 102.2 0 Td[(a)]TJ/F20 16.53 Tf 11.19 8.22 Td[(m)]TJ/F21 13.77 Tf 15.53 -3.41 Td[(j)]TJ/F22 19.83 Tf 13.56 -4.81 Td[(6)]TJ/F15 19.83 Tf 22.25 0 Td[(1)-417(\050)]TJ/F19 19.83 Tf 30.3 0 Td[(q)]TJ/F15 19.83 Tf 10.11 0 Td[(\051.)]TJ -352.64 -57.79 Td[(Then)]TJ/F19 19.83 Tf 61.84 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.71 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(a)]TJ/F20 16.53 Tf 11.19 8.23 Td[(m)]TJ/F21 13.77 Tf 15.53 -3.41 Td[(j)]TJ/F22 19.83 Tf 12.39 -4.82 Td[( )]TJ/F15 19.83 Tf 21.08 0 Td[(1)]TJ/F19 19.83 Tf 12.39 0 Td[(;)-177(N)]TJ/F15 19.83 Tf 28.2 0 Td[(\051)-296(=)]TJ/F19 19.83 Tf 40.63 0 Td[(p:)]TJ/F15 19.83 Tf -263.6 -57.78 Td[(Here's)-416(an)-417(example)-416(fo)35(r)]TJ/F19 19.83 Tf 229.45 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-296(20701)]TJ/F19 19.83 Tf 87.11 0 Td[(:)]TJ ET endstream endobj 87 0 obj 2093 endobj 84 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F20 12 0 R /F21 12 0 R >> /ProcSet [/PDF /Text] >> endobj 85 0 obj << /Type /Page /Contents 86 0 R /Resources 84 0 R /MediaBox [0 0 595.27 841.89] /Parent 88 0 R >> endobj 91 0 obj << /Length 92 0 R >> stream 1 0 0 1 113.2 708.12 cm BT /F15 19.83 Tf 0 0 Td[(P)35(olla)35(rd's)]TJ/F19 19.83 Tf 94.61 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.08 0 Td[(1)-417(Metho)-35(d)-416(fo)34(r)]TJ/F19 19.83 Tf 142.82 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-296(20701)]TJ -339.31 -48.15 Td[(Pick)]TJ/F19 19.83 Tf 52.06 0 Td[(a)]TJ/F15 19.83 Tf 17.04 0 Td[(=)-296(2.)]TJ -69.1 -24.94 Td[(\050If)]TJ/F19 19.83 Tf 31.81 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.71 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(a;)-178(N)]TJ/F15 19.83 Tf 39.4 0 Td[(\051,)-417(that's)-419(an)-417(instant)-418(win.\051)]TJ -131.56 -48.15 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[(m)]TJ/F20 16.53 Tf 18.64 -4.1 Td[(j)]TJ/F15 19.83 Tf 14.4 4.1 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(LC)-71(M)]TJ/F15 19.83 Tf 53.1 0 Td[(\0501)]TJ/F19 19.83 Tf 22.03 0 Td[(;)]TJ/F15 19.83 Tf 9.37 0 Td[(2)]TJ/F19 19.83 Tf 12.4 0 Td[(;)-177(:)-177(:)-178(:)-177(;)-177(j)]TJ/F15 19.83 Tf 56.49 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ/F15 19.83 Tf -263.49 -48.15 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[(X)]TJ/F20 16.53 Tf 17.33 -4.1 Td[(j)]TJ/F15 19.83 Tf 14.41 4.1 Td[(=)-295(2)]TJ/F20 16.53 Tf 37.53 8.22 Td[(m)]TJ/F21 13.77 Tf 15.53 -3.41 Td[(j)]TJ/F15 19.83 Tf 15.97 -4.81 Td[(reduced)-416(mo)-35(dulo)]TJ/F19 19.83 Tf 170.09 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(.)]TJ -331.98 -48.16 Td[(Let)]TJ/F19 19.83 Tf 42.28 0 Td[(F)]TJ/F20 16.53 Tf 13.33 -4.09 Td[(j)]TJ/F15 19.83 Tf 14.41 4.09 Td[(=)]TJ/F19 19.83 Tf 25.13 0 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.72 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(X)]TJ/F20 16.53 Tf 17.33 -4.09 Td[(j)]TJ/F22 19.83 Tf 13.23 4.09 Td[( )]TJ/F15 19.83 Tf 21.08 0 Td[(1)]TJ/F19 19.83 Tf 12.39 0 Td[(;)-177(N)]TJ/F15 19.83 Tf 28.21 0 Td[(\051.)]TJ/F19 19.83 Tf -115.88 -38.96 Td[(j)]TJ ET 108.39 -263.82 0.6 24.25 re f 1 0 0 1 139.04 -256.51 cm BT /F19 19.83 Tf 0 0 Td[(m)]TJ/F20 16.53 Tf 18.64 -4.09 Td[(j)]TJ ET 34.87 -7.31 0.6 24.25 re f 1 0 0 1 79.23 0 cm BT /F19 19.83 Tf 0 0 Td[(X)]TJ/F20 16.53 Tf 17.33 -4.09 Td[(j)]TJ ET 33.55 -7.31 0.6 24.25 re f 1 0 0 1 57.12 0 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ/F20 16.53 Tf 13.34 -4.09 Td[(j)]TJ ET -195.04 -7.9 224.9 0.6 re f 1 0 0 1 -187.07 -24.84 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 77.92 0 cm BT /F15 19.83 Tf 0 0 Td[(4)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 53.12 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -204.53 -7.57 224.9 0.6 re f 1 0 0 1 -196.56 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(6)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(64)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -204.53 -7.57 224.9 0.6 re f 1 0 0 1 -196.56 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(4)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 53.12 0 cm BT /F15 19.83 Tf 0 0 Td[(12)]TJ ET 32.47 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(4096)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 90.31 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -204.53 -7.57 224.9 0.6 re f 1 0 0 1 -196.56 -24.5 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 53.12 0 cm BT /F15 19.83 Tf 0 0 Td[(60)]TJ ET 32.47 -6.98 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(6493)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 90.31 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -204.53 -7.58 224.9 0.6 re f 1 0 0 1 -196.56 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(6)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 53.12 0 cm BT /F15 19.83 Tf 0 0 Td[(60)]TJ ET 32.47 -6.98 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(6493)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 90.31 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -204.53 -7.57 224.9 0.6 re f 1 0 0 1 -196.56 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(420)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(17273)]TJ ET 69.64 -6.97 0.6 23.91 re f 1 0 0 1 77.91 0 cm BT /F15 19.83 Tf 0 0 Td[(127)]TJ ET -179.74 -7.57 224.9 0.6 re f 1 0 0 1 -171.77 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(8)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(840)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(13717)]TJ ET 69.64 -6.97 0.6 23.91 re f 1 0 0 1 77.91 0 cm BT /F15 19.83 Tf 0 0 Td[(127)]TJ ET -179.74 -7.57 224.9 0.6 re f 1 0 0 1 -171.77 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(9)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(2520)]TJ ET 57.26 -6.97 0.6 23.91 re f 1 0 0 1 77.92 0 cm BT /F15 19.83 Tf 0 0 Td[(6986)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(127)]TJ ET -179.74 -7.57 224.9 0.6 re f 1 0 0 1 -300.91 -54.09 cm BT /F15 19.83 Tf 0 0 Td[(So)]TJ/F19 19.83 Tf 34.43 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-295(127)]TJ/F22 19.83 Tf 67 0 Td[()]TJ/F15 19.83 Tf 10.54 0 Td[(163)]TJ/F19 19.83 Tf 37.18 0 Td[(:)]TJ/F15 19.83 Tf -173.84 -48.15 Td[(Next:)-555(another)-417(example.)]TJ ET endstream endobj 92 0 obj 5093 endobj 89 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F20 12 0 R /F21 12 0 R >> /ProcSet [/PDF /Text] >> endobj 90 0 obj << /Type /Page /Contents 91 0 R /Resources 89 0 R /MediaBox [0 0 595.27 841.89] /Parent 88 0 R >> endobj 95 0 obj << /Length 96 0 R >> stream 1 0 0 1 119.39 678.42 cm BT /F15 19.83 Tf 0 0 Td[(P)35(olla)34(rd's)]TJ/F19 19.83 Tf 94.62 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)-417(Metho)-35(d)-417(fo)35(r)]TJ/F19 19.83 Tf 142.83 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-295(5029)]TJ/F19 19.83 Tf -193.6 -86.68 Td[(j)]TJ ET 122.24 -93.99 0.6 24.25 re f 1 0 0 1 152.9 -86.68 cm BT /F19 19.83 Tf 0 0 Td[(m)]TJ/F20 16.53 Tf 18.64 -4.09 Td[(j)]TJ ET 34.86 -7.31 0.6 24.25 re f 1 0 0 1 66.83 0 cm BT /F19 19.83 Tf 0 0 Td[(X)]TJ/F20 16.53 Tf 17.33 -4.09 Td[(j)]TJ ET 33.55 -7.31 0.6 24.25 re f 1 0 0 1 41.82 0 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ/F20 16.53 Tf 13.34 -4.09 Td[(j)]TJ ET -179.74 -7.9 209.6 0.6 re f 1 0 0 1 -159.38 -24.84 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 65.53 0 cm BT /F15 19.83 Tf 0 0 Td[(4)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 37.82 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -168.87 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(6)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(64)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 50.22 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -168.87 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(4)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(12)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(4096)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -168.87 -24.5 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(60)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1156)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.58 209.6 0.6 re f 1 0 0 1 -168.87 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(6)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(60)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(6493)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -168.87 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(420)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(4153)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -168.87 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(8)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(840)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 53.13 0 cm BT /F15 19.83 Tf 0 0 Td[(2968)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -168.87 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(9)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(2520)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 77.92 0 cm BT /F15 19.83 Tf 0 0 Td[(625)]TJ ET 44.85 -6.97 0.6 23.91 re f 1 0 0 1 62.61 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -181.26 -24.5 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.98 0.6 23.91 re f 97.98 -6.98 0.6 23.91 re f 1 0 0 1 106.25 0 cm BT /F15 19.83 Tf 0 0 Td[(4920)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.58 209.6 0.6 re f 1 0 0 1 -181.26 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.98 0.6 23.91 re f 97.98 -6.98 0.6 23.91 re f 1 0 0 1 106.25 0 cm BT /F15 19.83 Tf 0 0 Td[(4327)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -181.26 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(16)]TJ ET 32.46 -6.97 0.6 23.91 re f 97.98 -6.97 0.6 23.91 re f 1 0 0 1 106.25 0 cm BT /F15 19.83 Tf 0 0 Td[(4991)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -181.26 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.46 -6.97 0.6 23.91 re f 97.98 -6.97 0.6 23.91 re f 1 0 0 1 118.65 0 cm BT /F15 19.83 Tf 0 0 Td[(850)]TJ ET 44.85 -6.97 0.6 23.91 re f 1 0 0 1 62.61 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -181.26 -24.51 cm BT /F15 19.83 Tf 0 0 Td[(19)]TJ ET 32.46 -6.97 0.6 23.91 re f 97.98 -6.97 0.6 23.91 re f 1 0 0 1 106.25 0 cm BT /F15 19.83 Tf 0 0 Td[(2077)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 75.01 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET -189.23 -7.57 209.6 0.6 re f 1 0 0 1 -318.05 -63.18 cm BT /F15 19.83 Tf 0 0 Td[(Better)-416(luck)-417(with)-417(the)-417(next)-416(metho)-36(d!)]TJ ET endstream endobj 96 0 obj 4872 endobj 93 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F20 12 0 R >> /ProcSet [/PDF /Text] >> endobj 94 0 obj << /Type /Page /Contents 95 0 R /Resources 93 0 R /MediaBox [0 0 595.27 841.89] /Parent 88 0 R >> endobj 99 0 obj << /Length 100 0 R >> stream 1 0 0 1 123.44 633.07 cm BT /F15 19.83 Tf 0 0 Td[(P)35(olla)35(rd's)]TJ/F19 19.83 Tf 94.62 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)-417(Metho)-35(d)-417(P)35(erfo)36(rmance)]TJ -182.04 -57.79 Td[(P)35(olla)35(rd's)-278(metho)-36(d)-278(\014nds)-278(facto)35(rs)]TJ/F19 19.83 Tf 301.62 0 Td[(p)]TJ/F15 19.83 Tf 16.11 0 Td[(such)-278(that)-279(p)34(rime)]TJ -317.73 -27.89 Td[(p)-35(o)35(w)34(er)-416(facto)34(rs)-416(of)]TJ/F19 19.83 Tf 173.39 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.08 0 Td[(1)-417(a)35(re)-416(all)-417(small.)]TJ -209.76 -57.78 Td[(T)104(ypical)-548(size)-548(of)-549(la)34(rgest)-548(p)34(rime)-548(p)-35(o)35(w)34(er)-548(facto)34(r)-548(of)]TJ/F19 19.83 Tf 0 -27.9 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)-417(is)]TJ/F19 19.83 Tf 100.8 -37.86 Td[(p)]TJ/F17 16.53 Tf 10.61 8.24 Td[(1)]TJ/F23 16.53 Tf 10.33 0 Td[( )]TJ/F17 16.53 Tf 13.66 0 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=e)]TJ/F22 19.83 Tf 23.28 -8.24 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(N)]TJ/F17 16.53 Tf 18.84 8.24 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=e)]TJ/F23 16.53 Tf 16.92 0 Td[( )]TJ/F17 16.53 Tf 13.66 0 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=e)]TJ/F18 13.77 Tf 16.93 5.83 Td[(2)]TJ/F19 19.83 Tf 9.6 -14.07 Td[(:)]TJ/F15 19.83 Tf -324.22 -67.74 Td[(So:)-693(P)34(olla)35(rd's)-486(metho)-35(d)-486(is)-486(slo)35(w)-487(against)-487(a)-486(sma)34(rt)]TJ 0 -27.9 Td[(adversa)35(ry)105(.)]TJ ET endstream endobj 100 0 obj 1450 endobj 97 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F17 5 0 R /F23 13 0 R /F20 12 0 R /F18 5 0 R >> /ProcSet [/PDF /Text] >> endobj 98 0 obj << /Type /Page /Contents 99 0 R /Resources 97 0 R /MediaBox [0 0 595.27 841.89] /Parent 88 0 R >> endobj 103 0 obj << /Length 104 0 R >> stream 1 0 0 1 123.44 657.23 cm BT /F15 19.83 Tf 0 0 Td[(P)35(olla)35(rd's)]TJ/F19 19.83 Tf 94.62 0 Td[(p)]TJ/F22 19.83 Tf 15.29 0 Td[( )]TJ/F15 19.83 Tf 21.07 0 Td[(1)-417(Metho)-35(d)-417(P)35(erfo)36(rmance)]TJ -182.04 -57.78 Td[(The)-416(adversa)35(ry)-417(already)-416(cho)-34(oses:)]TJ/F19 19.83 Tf 0 -57.78 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)]TJ/F19 19.83 Tf 25.13 0 Td[(pq)]TJ/F15 19.83 Tf 20.73 0 Td[(,)-417(the)-417(p)35(ro)-35(duct)-417(of)-416(exactly)-416(t)34(w)34(o)-417(p)35(rimes,)]TJ/F19 19.83 Tf -70.55 -57.79 Td[(p;)-177(q)]TJ/F15 19.83 Tf 38.35 0 Td[(a)34(re)-416(not)-417(small.)]TJ/F19 19.83 Tf -38.35 -57.78 Td[(p;)-177(q)]TJ/F15 19.83 Tf 38.35 0 Td[(a)34(re)-416(not)-417(to)-35(o)-417(close)-416(to)]TJ/F22 19.83 Tf 210.59 16.68 Td[(p)]TJ ET 215.44 -214.45 18.84 0.89 re f 1 0 0 1 215.44 -231.13 cm BT /F19 19.83 Tf 0 0 Td[(N)]TJ/F15 19.83 Tf -266.5 -57.78 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(p)]TJ/F22 19.83 Tf 16.46 0 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(N)]TJ/F17 16.53 Tf 18.84 7 Td[(1)]TJ/F20 16.53 Tf 10.33 0 Td[(=e)]TJ/F15 19.83 Tf 17.42 -7 Td[(\051)]TJ -94.93 -85.68 Td[(No)35(w)-420(add:)]TJ/F19 19.83 Tf 107.21 0 Td[(p)]TJ/F22 19.83 Tf 15.33 0 Td[( )]TJ/F15 19.83 Tf 21.11 0 Td[(1)]TJ/F19 19.83 Tf 12.4 0 Td[(;)-177(q)]TJ/F22 19.83 Tf 24.2 0 Td[( )]TJ/F15 19.83 Tf 21.12 0 Td[(1)-420(each)-420(have)-420(at)-421(least)-420(some)]TJ -201.37 -27.9 Td[(la)35(rge)-416(p)34(rime)-416(p)-35(o)35(w)34(er)-416(facto)34(r.)]TJ ET endstream endobj 104 0 obj 1453 endobj 101 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F17 5 0 R /F20 12 0 R >> /ProcSet [/PDF /Text] >> endobj 102 0 obj << /Type /Page /Contents 103 0 R /Resources 101 0 R /MediaBox [0 0 595.27 841.89] /Parent 88 0 R >> endobj 107 0 obj << /Length 108 0 R >> stream 1 0 0 1 190.34 695.58 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(Metho)-35(d)]TJ -117.96 -57.78 Td[(Given)]TJ/F19 19.83 Tf 64.73 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(,)-417(let's)-417(solve)]TJ/F19 19.83 Tf 139.51 0 Td[(x)]TJ/F17 16.53 Tf 11.86 7 Td[(2)]TJ/F22 19.83 Tf 16.69 -7 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(y)]TJ/F17 16.53 Tf 11.13 7 Td[(2)]TJ/F15 19.83 Tf 19.09 -7 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051.)]TJ -332.57 -57.78 Td[(Metho)-35(d:)]TJ 0 -57.79 Td[(Find)-454(lots)-455(of)-455(integers)]TJ/F19 19.83 Tf 216.46 0 Td[(a)]TJ/F15 19.83 Tf 20.2 0 Td[(such)-455(that)]TJ/F19 19.83 Tf 105.35 0 Td[(a)]TJ/F15 19.83 Tf 20.2 0 Td[(and)]TJ/F19 19.83 Tf 45.51 0 Td[(N)]TJ/F15 19.83 Tf 23.94 0 Td[(+)]TJ/F19 19.83 Tf 24.39 0 Td[(a)]TJ/F15 19.83 Tf -456.05 -27.89 Td[(have)-416(only)-417(small)-417(p)35(rime)-416(facto)34(rs.)]TJ 0 -57.79 Td[(Pick)-416(a)-417(subset)-418(of)-416(the)]TJ/F19 19.83 Tf 212.92 0 Td[(a)]TJ/F23 16.53 Tf 11.19 7 Td[(0)]TJ/F19 19.83 Tf 5.27 -7 Td[(s)]TJ/F15 19.83 Tf 18 0 Td[(such)-417(that)]TJ/F25 17.22 Tf -126.03 -25.83 Td[(Y)]TJ/F20 16.53 Tf 8.01 -39.62 Td[(i)]TJ/F19 19.83 Tf 17.5 22.61 Td[(a)]TJ/F20 16.53 Tf 11.19 -4.09 Td[(i)]TJ/F19 19.83 Tf 6.48 4.09 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(\050)]TJ/F19 19.83 Tf 9.65 0 Td[(N)]TJ/F15 19.83 Tf 23.52 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(a)]TJ/F20 16.53 Tf 11.19 -4.09 Td[(i)]TJ/F15 19.83 Tf 6.48 4.09 Td[(\051)-295(=)]TJ/F19 19.83 Tf 40.63 0 Td[(s)]TJ/F17 16.53 Tf 9.74 8.24 Td[(2)]TJ/F19 19.83 Tf 10.83 -8.24 Td[(=t)]TJ/F17 16.53 Tf 18.15 8.24 Td[(2)]TJ/F19 19.83 Tf 10.83 -8.24 Td[(:)]TJ/F15 19.83 Tf -340.04 -79.94 Td[(Conclude:)-555(F)35(o)34(r)]TJ/F19 19.83 Tf 153.15 0 Td[(x)]TJ/F15 19.83 Tf 17.71 0 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(s)]TJ/F15 19.83 Tf 9.74 0 Td[(,)]TJ/F19 19.83 Tf 15.15 0 Td[(y)]TJ/F15 19.83 Tf 16.98 0 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(t)]TJ/F15 19.83 Tf 7.61 0 Td[(,)]TJ/F19 19.83 Tf -99.49 -42.84 Td[(x)]TJ/F17 16.53 Tf 11.86 8.24 Td[(2)]TJ/F22 19.83 Tf 16.68 -8.24 Td[()]TJ/F19 19.83 Tf 22.25 0 Td[(y)]TJ/F17 16.53 Tf 11.12 8.24 Td[(2)]TJ/F15 19.83 Tf 19.1 -8.24 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(:)]TJ -290.25 -67.75 Td[(GC)-71(D)]TJ/F15 19.83 Tf 50.71 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(x)]TJ/F22 19.83 Tf 18.15 0 Td[( )]TJ/F19 19.83 Tf 22.68 0 Td[(y)-36(;)-178(N)]TJ/F15 19.83 Tf 39.33 0 Td[(\051)-560(has)-561(even)-559(o)-34(dds)-561(to)-560(b)-35(e)-560(a)-560(p)35(rime)]TJ -140.51 -27.89 Td[(diviso)35(r)-416(of)]TJ/F19 19.83 Tf 100.4 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(.)]TJ ET endstream endobj 108 0 obj 2621 endobj 105 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F17 5 0 R /F22 13 0 R /F23 13 0 R /F25 45 0 R /F20 12 0 R >> /ProcSet [/PDF /Text] >> endobj 106 0 obj << /Type /Page /Contents 107 0 R /Resources 105 0 R /MediaBox [0 0 595.27 841.89] /Parent 88 0 R >> endobj 111 0 obj << /Length 112 0 R >> stream 1 0 0 1 173.54 657.23 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(V)35(o)-34(cabula)34(ry)]TJ -101.16 -57.78 Td[(Given)]TJ/F19 19.83 Tf 64.73 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(,)-417(w)35(e)-417(pick)]TJ/F19 19.83 Tf 99.16 0 Td[(B)]TJ/F15 19.83 Tf 16.87 0 Td[(,)-417(the)]TJ/F32 19.83 Tf 55.78 0 Td[(smo)-35(othness)-418(b)-35(ound)]TJ/F15 19.83 Tf 188.96 0 Td[(.)]TJ -444.34 -57.78 Td[(W)35(e)-416(treat)-418(a)-417(p)35(rime)]TJ/F19 19.83 Tf 182.62 0 Td[(p)]TJ/F15 19.83 Tf 18.87 0 Td[(less)-417(than)]TJ/F19 19.83 Tf 97.51 0 Td[(B)]TJ/F15 19.83 Tf 25.14 0 Td[(as)-417(small.)]TJ -324.14 -57.79 Td[(An)-376(integer)]TJ/F19 19.83 Tf 112.86 0 Td[(a)]TJ/F15 19.83 Tf 18.66 0 Td[(is)]TJ/F19 19.83 Tf 22.48 0 Td[(B)]TJ/F15 19.83 Tf 16.87 0 Td[(-smo)-35(oth)-377(means)-377(every)-375(p)34(rime)]TJ/F19 19.83 Tf 285.76 0 Td[(p)]TJ/F15 19.83 Tf -456.63 -27.89 Td[(dividing)]TJ/F19 19.83 Tf 85.39 0 Td[(a)]TJ/F15 19.83 Tf 19.45 0 Td[(is)-417(less)-417(than)]TJ/F19 19.83 Tf 120.79 0 Td[(B)]TJ/F15 19.83 Tf 16.87 0 Td[(.)]TJ -242.5 -57.79 Td[(The)-416(set)]TJ/F22 19.83 Tf 87.18 0 Td[(B)]TJ/F15 19.83 Tf 22.57 0 Td[(of)-417(small)-417(p)34(rimes)-416(is)-417(the)]TJ/F32 19.83 Tf 225.46 0 Td[(facto)34(r)-416(base)]TJ/F15 19.83 Tf 112.11 0 Td[(.)]TJ -447.32 -57.78 Td[(A)-397(pair)-398(\050)]TJ/F19 19.83 Tf 79.27 0 Td[(a;)-178(N)]TJ/F15 19.83 Tf 43.45 0 Td[(+)]TJ/F19 19.83 Tf 23.33 0 Td[(a)]TJ/F15 19.83 Tf 11.19 0 Td[(\051)-398(of)-398(smo)-36(oth)-398(numb)-36(ers)-397(is)-398(a)]TJ/F32 19.83 Tf 265.24 0 Td[(rela-)]TJ -422.48 -27.89 Td[(tion)]TJ/F15 19.83 Tf 47.51 0 Td[(o)35(r)]TJ/F32 19.83 Tf 28.24 0 Td[(smo)-35(oth)-417(relation)]TJ/F15 19.83 Tf 159.62 0 Td[(.)]TJ -235.37 -57.79 Td[(Here)-415(is)-417(an)-417(example)-416(with)]TJ/F19 19.83 Tf 252.17 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-296(5029,)]TJ/F19 19.83 Tf 89.87 0 Td[(B)]TJ/F15 19.83 Tf 22.73 0 Td[(=)-295(20.)]TJ ET endstream endobj 112 0 obj 1895 endobj 109 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F32 18 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 110 0 obj << /Type /Page /Contents 111 0 R /Resources 109 0 R /MediaBox [0 0 595.27 841.89] /Parent 113 0 R >> endobj 116 0 obj << /Length 117 0 R >> stream 1 0 0 1 161.78 708.12 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(fo)35(r)]TJ/F19 19.83 Tf 189.03 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-296(5029)]TJ -303.12 -49.7 Td[(F)35(acto)34(r)]TJ/F19 19.83 Tf 73.95 0 Td[(N)]TJ/F15 19.83 Tf 24.7 0 Td[(=)-295(5029.)]TJ -98.65 -49.7 Td[(F)35(acto)34(r)-416(base)]TJ/F22 19.83 Tf 126.84 0 Td[(B)]TJ/F15 19.83 Tf 20.17 0 Td[(=)]TJ/F22 19.83 Tf 25.13 0 Td[(f)]TJ/F15 19.83 Tf 10.54 0 Td[(2)]TJ/F19 19.83 Tf 12.39 0 Td[(;)]TJ/F15 19.83 Tf 9.37 0 Td[(3)]TJ/F19 19.83 Tf 12.39 0 Td[(;)]TJ/F15 19.83 Tf 9.37 0 Td[(5)]TJ/F19 19.83 Tf 12.4 0 Td[(;)]TJ/F15 19.83 Tf 9.36 0 Td[(7)]TJ/F19 19.83 Tf 12.4 0 Td[(;)]TJ/F15 19.83 Tf 9.36 0 Td[(11)]TJ/F19 19.83 Tf 24.79 0 Td[(;)]TJ/F15 19.83 Tf 9.37 0 Td[(13)]TJ/F19 19.83 Tf 24.79 0 Td[(;)]TJ/F15 19.83 Tf 9.36 0 Td[(17)]TJ/F19 19.83 Tf 24.8 0 Td[(;)]TJ/F15 19.83 Tf 9.36 0 Td[(19)]TJ/F22 19.83 Tf 24.79 0 Td[(g)]TJ/F19 19.83 Tf 10.54 0 Td[(:)]TJ ET -40.7 -188.07 0.6 23.91 re f 1 0 0 1 -6.43 -181.1 cm BT /F19 19.83 Tf 0 0 Td[(a)]TJ ET 18.86 -6.97 0.6 23.91 re f 1 0 0 1 27.13 0 cm BT /F19 19.83 Tf 0 0 Td[(a)]TJ/F15 19.83 Tf 15.87 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(N)]TJ ET 66.35 -6.97 0.6 23.91 re f 1 0 0 1 74.62 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(19)]TJ ET 32.46 -6.97 0.6 23.91 re f -406.02 -7.57 438.79 0.6 re f 1 0 0 1 -395 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.45 -6.97 0.6 23.91 re f 1 0 0 1 44.12 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 49.83 0 cm BT /F15 19.83 Tf 0 0 Td[(5040)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -402.29 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(B)]TJ ET 24.54 -6.97 0.6 23.91 re f 1 0 0 1 45.21 0 cm BT /F15 19.83 Tf 0 0 Td[(20)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 49.83 0 cm BT /F15 19.83 Tf 0 0 Td[(5049)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -401.84 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(C)]TJ ET 24.09 -6.98 0.6 23.91 re f 1 0 0 1 44.76 0 cm BT /F15 19.83 Tf 0 0 Td[(25)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 49.83 0 cm BT /F15 19.83 Tf 0 0 Td[(5054)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -412.22 -7.58 438.79 0.6 re f 1 0 0 1 -403.29 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(D)]TJ ET 25.54 -6.98 0.6 23.91 re f 1 0 0 1 46.21 0 cm BT /F15 19.83 Tf 0 0 Td[(91)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 49.83 0 cm BT /F15 19.83 Tf 0 0 Td[(5120)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -401.97 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(E)]TJ ET 24.22 -6.97 0.6 23.91 re f 1 0 0 1 32.49 0 cm BT /F15 19.83 Tf 0 0 Td[(119)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5148)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -401.68 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ ET 23.93 -6.97 0.6 23.91 re f 1 0 0 1 32.2 0 cm BT /F15 19.83 Tf 0 0 Td[(171)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5200)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -401.84 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(G)]TJ ET 24.09 -6.97 0.6 23.91 re f 1 0 0 1 32.36 0 cm BT /F15 19.83 Tf 0 0 Td[(196)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5225)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -404.25 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(H)]TJ ET 26.5 -6.98 0.6 23.91 re f 1 0 0 1 34.77 0 cm BT /F15 19.83 Tf 0 0 Td[(221)]TJ ET 44.86 -6.98 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5250)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -412.22 -7.58 438.79 0.6 re f 1 0 0 1 -396.1 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(I)]TJ ET 18.35 -6.98 0.6 23.91 re f 1 0 0 1 26.62 0 cm BT /F15 19.83 Tf 0 0 Td[(275)]TJ ET 44.86 -6.98 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5304)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -426.45 -55.73 cm BT /F15 19.83 Tf 0 0 Td[(Eliminate)-417(19)-417(with)]TJ/F19 19.83 Tf 188.27 0 Td[(F)]TJ/F15 19.83 Tf 20.94 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(G)]TJ/F15 19.83 Tf 24.68 0 Td[(replacing)]TJ/F19 19.83 Tf 98.48 0 Td[(F)-30(;)-177(G)]TJ/F15 19.83 Tf 39.7 0 Td[(.)]TJ -396.04 -49.69 Td[(Eliminate)-443(2)-442(and)-443(3)-443(with)]TJ/F19 19.83 Tf 243.86 0 Td[(B)]TJ/F15 19.83 Tf 21.84 0 Td[(+)]TJ/F19 19.83 Tf 24.26 0 Td[(C)]TJ/F15 19.83 Tf 21.39 0 Td[(+)]TJ/F19 19.83 Tf 24.25 0 Td[(H)]TJ/F15 19.83 Tf 27.62 0 Td[(and)]TJ/F19 19.83 Tf 45.27 0 Td[(H)]TJ/F15 19.83 Tf 23.81 0 Td[(+)]TJ/F19 19.83 Tf 24.26 0 Td[(I)]TJ/F15 19.83 Tf -456.56 -25.41 Td[(replacing)]TJ/F19 19.83 Tf 98.47 0 Td[(B)-49(;)-177(C)-12(;)-177(H)-18(;)-178(I)]TJ/F15 19.83 Tf 88.57 0 Td[(.)]TJ ET endstream endobj 117 0 obj 10937 endobj 114 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 115 0 obj << /Type /Page /Contents 116 0 R /Resources 114 0 R /MediaBox [0 0 595.27 841.89] /Parent 113 0 R >> endobj 120 0 obj << /Length 121 0 R >> stream 1 0 0 1 72.38 708.12 cm BT /F15 19.83 Tf 0 0 Td[(Eliminate)-417(19)-417(with)]TJ/F19 19.83 Tf 188.27 0 Td[(F)]TJ/F15 19.83 Tf 20.94 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(G)]TJ/F15 19.83 Tf 16.42 0 Td[(.)]TJ -249.6 -23.91 Td[(Eliminate)-412(2)-412(and)-413(3)-412(with)]TJ/F19 19.83 Tf 240.84 0 Td[(B)]TJ/F15 19.83 Tf 21.4 0 Td[(+)]TJ/F19 19.83 Tf 23.81 0 Td[(C)]TJ/F15 19.83 Tf 20.95 0 Td[(+)]TJ/F19 19.83 Tf 23.81 0 Td[(H)]TJ/F15 19.83 Tf 27.01 0 Td[(and)]TJ/F19 19.83 Tf 44.67 0 Td[(H)]TJ/F15 19.83 Tf 23.37 0 Td[(+)]TJ/F19 19.83 Tf 23.81 0 Td[(I)]TJ/F15 19.83 Tf 10.69 0 Td[(.)]TJ ET 206.57 -64.52 0.6 23.91 re f 1 0 0 1 214.84 -57.55 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.46 -6.97 0.6 23.91 re f -271.46 -7.57 304.23 0.6 re f 1 0 0 1 -169.85 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.45 -6.97 0.6 23.91 re f 1 0 0 1 31.72 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -277.66 -7.57 304.23 0.6 re f 1 0 0 1 -178.14 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(D)]TJ ET 25.54 -6.97 0.6 23.91 re f 1 0 0 1 33.81 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -277.66 -7.57 304.23 0.6 re f 1 0 0 1 -176.83 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(E)]TJ ET 24.23 -6.98 0.6 23.91 re f 1 0 0 1 32.5 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f -277.66 -7.58 304.23 0.6 re f 1 0 0 1 -221.6 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ/F15 19.83 Tf 20.94 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(G)]TJ ET 69 -6.98 0.6 23.91 re f 1 0 0 1 77.27 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -277.66 -7.57 304.23 0.6 re f 1 0 0 1 -269.69 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(B)]TJ/F15 19.83 Tf 21.55 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(C)]TJ/F15 19.83 Tf 21.11 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(H)]TJ ET 117.09 -6.97 0.6 23.91 re f 1 0 0 1 125.36 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -277.66 -7.57 304.23 0.6 re f 1 0 0 1 -218.44 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(H)]TJ/F15 19.83 Tf 23.52 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(I)]TJ ET 65.84 -6.97 0.6 23.91 re f 1 0 0 1 74.11 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -277.66 -7.57 304.23 0.6 re f 1 0 0 1 -359.17 -51.23 cm BT /F15 19.83 Tf 0 0 Td[(Only)-416(ro)34(w)]TJ/F19 19.83 Tf 101.09 0 Td[(E)]TJ/F15 19.83 Tf 24.82 0 Td[(has)-417(17,)-417(so)-417(strik)34(e)-417(it.)]TJ ET 226.94 -40.61 0.6 23.91 re f 1 0 0 1 235.2 -33.64 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.97 0.6 23.91 re f -230.74 -7.57 263.5 0.6 re f 1 0 0 1 -171.51 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(H)]TJ/F15 19.83 Tf 23.52 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(I)]TJ ET 65.84 -6.97 0.6 23.91 re f 1 0 0 1 74.1 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.27 -6.97 0.6 23.91 re f -236.93 -7.57 263.5 0.6 re f 1 0 0 1 -135.32 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.46 -6.98 0.6 23.91 re f 1 0 0 1 31.72 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.27 -6.98 0.6 23.91 re f -236.93 -7.58 263.5 0.6 re f 1 0 0 1 -137.41 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(D)]TJ ET 25.55 -6.98 0.6 23.91 re f 1 0 0 1 33.81 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.27 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.98 0.6 23.91 re f -236.93 -7.57 263.5 0.6 re f 1 0 0 1 -180.86 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ/F15 19.83 Tf 20.94 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(G)]TJ ET 69 -6.97 0.6 23.91 re f 1 0 0 1 77.26 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.97 0.6 23.91 re f -236.93 -7.57 263.5 0.6 re f 1 0 0 1 -228.96 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(B)]TJ/F15 19.83 Tf 21.56 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(C)]TJ/F15 19.83 Tf 21.1 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(H)]TJ ET 117.1 -6.97 0.6 23.91 re f 1 0 0 1 125.36 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.97 0.6 23.91 re f -236.93 -7.57 263.5 0.6 re f 1 0 0 1 -338.8 -51.23 cm BT /F15 19.83 Tf 0 0 Td[(Relations:)]TJ/F19 19.83 Tf 0 -44.83 Td[(A)]TJ/F15 19.83 Tf 20.46 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(H)]TJ/F15 19.83 Tf 23.52 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(I)]TJ -91.91 -23.91 Td[(A)]TJ/F15 19.83 Tf 20.46 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(D)]TJ/F15 19.83 Tf 22.55 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(F)]TJ/F15 19.83 Tf 20.94 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(G)]TJ -135.86 -23.91 Td[(B)]TJ/F15 19.83 Tf 21.55 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(C)]TJ/F15 19.83 Tf 21.11 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(F)]TJ/F15 19.83 Tf 20.95 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(G)]TJ/F15 19.83 Tf 21.1 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(H)]TJ ET endstream endobj 121 0 obj 8097 endobj 118 0 obj << /Font << /F15 5 0 R /F19 12 0 R >> /ProcSet [/PDF /Text] >> endobj 119 0 obj << /Type /Page /Contents 120 0 R /Resources 118 0 R /MediaBox [0 0 595.27 841.89] /Parent 113 0 R >> endobj 124 0 obj << /Length 125 0 R >> stream 1 0 0 1 161.78 708.12 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(fo)35(r)]TJ/F19 19.83 Tf 189.03 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-296(5029)]TJ -303.12 -49.09 Td[(Assembling)-416(relations:)]TJ ET -40.7 -90.68 0.6 23.91 re f 1 0 0 1 -6.43 -83.71 cm BT /F19 19.83 Tf 0 0 Td[(a)]TJ ET 18.86 -6.97 0.6 23.91 re f 1 0 0 1 27.13 0 cm BT /F19 19.83 Tf 0 0 Td[(a)]TJ/F15 19.83 Tf 15.87 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(N)]TJ ET 66.35 -6.97 0.6 23.91 re f 1 0 0 1 74.62 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(19)]TJ ET 32.46 -6.97 0.6 23.91 re f -406.02 -7.57 438.79 0.6 re f 1 0 0 1 -395 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.45 -6.98 0.6 23.91 re f 1 0 0 1 44.12 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 49.83 0 cm BT /F15 19.83 Tf 0 0 Td[(5040)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -404.25 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(H)]TJ ET 26.5 -6.98 0.6 23.91 re f 1 0 0 1 34.77 0 cm BT /F15 19.83 Tf 0 0 Td[(221)]TJ ET 44.86 -6.98 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5250)]TJ ET 57.25 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -396.1 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(I)]TJ ET 18.35 -6.97 0.6 23.91 re f 1 0 0 1 26.62 0 cm BT /F15 19.83 Tf 0 0 Td[(275)]TJ ET 44.86 -6.97 0.6 23.91 re f 1 0 0 1 62.23 0 cm BT /F15 19.83 Tf 0 0 Td[(5304)]TJ ET 57.25 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.54 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -412.22 -7.57 438.79 0.6 re f 1 0 0 1 -426.45 -55.56 cm BT /F15 19.83 Tf 0 0 Td[(No)35(w)-417(compute)-417(over)]TJ/F34 20.66 Tf 199.29 0 Td[(Z)]TJ/F15 19.83 Tf 14.2 0 Td[(,)-417(not)-417(mo)-36(d)-416(2:)]TJ ET 34.47 -41.59 0.6 23.91 re f 1 0 0 1 45.66 -34.62 cm BT /F19 19.83 Tf 0 0 Td[(a=)]TJ/F15 19.83 Tf 21.72 0 Td[(\050)]TJ/F19 19.83 Tf 9.65 0 Td[(a)]TJ/F15 19.83 Tf 15.87 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(\051)]TJ ET 107.36 -6.97 0.6 23.91 re f 1 0 0 1 132.01 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.47 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(19)]TJ ET 32.46 -6.97 0.6 23.91 re f -470.37 -7.57 503.13 0.6 re f 1 0 0 1 -459.35 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.45 -6.97 0.6 23.91 re f 1 0 0 1 49.42 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ/F19 19.83 Tf 24.79 0 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(5040)]TJ ET 92.58 -6.97 0.6 23.91 re f 1 0 0 1 100.84 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(4)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(2)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 57.12 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f -482.76 -7.57 503.13 0.6 re f 1 0 0 1 -474.79 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(H)]TJ ET 26.51 -6.97 0.6 23.91 re f 1 0 0 1 40.07 0 cm BT /F15 19.83 Tf 0 0 Td[(221)]TJ/F19 19.83 Tf 37.19 0 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(5250)]TJ ET 104.98 -6.97 0.6 23.91 re f 1 0 0 1 113.24 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(3)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 57.12 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f -482.76 -7.57 503.13 0.6 re f 1 0 0 1 -466.64 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(I)]TJ ET 18.36 -6.98 0.6 23.91 re f 1 0 0 1 31.92 0 cm BT /F15 19.83 Tf 0 0 Td[(275)]TJ/F19 19.83 Tf 37.19 0 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(5304)]TJ ET 104.98 -6.98 0.6 23.91 re f 1 0 0 1 113.24 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(3)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 61.11 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.45 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 57.12 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f -482.76 -7.58 503.13 0.6 re f -448.28 -31.49 0.6 23.91 re f -329.74 -31.49 0.6 23.91 re f -285.02 -31.49 0.6 23.91 re f -240.29 -31.49 0.6 23.91 re f -195.57 -31.49 0.6 23.91 re f -150.84 -31.49 0.6 23.91 re f -110.11 -31.49 0.6 23.91 re f -65.39 -31.49 0.6 23.91 re f -20.66 -31.49 0.6 23.91 re f 20.07 -31.49 0.6 23.91 re f -448.28 -55.4 0.6 23.91 re f 1 0 0 1 -440.02 -48.42 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ/F15 19.83 Tf 20.47 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(H)]TJ/F15 19.83 Tf 23.53 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(I)]TJ ET 110.28 -6.98 0.6 23.91 re f 1 0 0 1 118.54 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(8)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(4)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(2)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(2)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 57.12 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f -482.76 -7.57 503.13 0.6 re f 1 0 0 1 -354.5 -76.57 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ/F17 16.53 Tf 24.79 8.24 Td[(2)]TJ/F22 19.83 Tf 16.68 -8.24 Td[()]TJ/F15 19.83 Tf 22.24 0 Td[(\0502)]TJ/F17 16.53 Tf 22.04 8.24 Td[(4)]TJ/F22 19.83 Tf 15.51 -8.24 Td[()]TJ/F15 19.83 Tf 10.54 0 Td[(3)]TJ/F17 16.53 Tf 12.39 8.24 Td[(2)]TJ/F22 19.83 Tf 15.51 -8.24 Td[()]TJ/F15 19.83 Tf 10.54 0 Td[(5)]TJ/F22 19.83 Tf 17.08 0 Td[()]TJ/F15 19.83 Tf 10.53 0 Td[(7\051)]TJ/F17 16.53 Tf 22.04 8.24 Td[(2)]TJ/F15 19.83 Tf -328.15 -67.29 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(x)]TJ/F15 19.83 Tf 17.71 0 Td[(=)-296(11)]TJ/F19 19.83 Tf 49.93 0 Td[(;)-177(y)]TJ/F15 19.83 Tf 26.35 0 Td[(=)-295(5040,)]TJ/F19 19.83 Tf 106.39 0 Td[(x)]TJ/F17 16.53 Tf 11.86 7 Td[(2)]TJ/F22 19.83 Tf 16.68 -7 Td[()]TJ/F19 19.83 Tf 22.25 0 Td[(y)]TJ/F17 16.53 Tf 11.12 7 Td[(2)]TJ/F15 19.83 Tf 19.09 -7 Td[(\050)]TJ/F19 19.83 Tf 9.65 0 Td[(N)]TJ/F15 19.83 Tf 18.83 0 Td[(\051.)]TJ -352.14 -49.08 Td[(Alas,)]TJ/F19 19.83 Tf 57.84 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)]TJ/F19 19.83 Tf 25.14 0 Td[(y)]TJ/F22 19.83 Tf 15.81 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(x)]TJ/F15 19.83 Tf 11.86 0 Td[(.)]TJ ET endstream endobj 125 0 obj 10586 endobj 122 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F34 83 0 R /F22 13 0 R /F17 5 0 R >> /ProcSet [/PDF /Text] >> endobj 123 0 obj << /Type /Page /Contents 124 0 R /Resources 122 0 R /MediaBox [0 0 595.27 841.89] /Parent 113 0 R >> endobj 128 0 obj << /Length 129 0 R >> stream 1 0 0 1 161.78 708.12 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(fo)35(r)]TJ/F19 19.83 Tf 189.03 0 Td[(N)]TJ/F15 19.83 Tf 24.69 0 Td[(=)-296(5029)]TJ -303.12 -55.36 Td[(Assembling)-416(relations:)]TJ ET -41.18 -98.4 0.6 23.91 re f 1 0 0 1 -6.92 -91.43 cm BT /F19 19.83 Tf 0 0 Td[(a)]TJ ET 18.87 -6.97 0.6 23.91 re f 1 0 0 1 27.14 0 cm BT /F19 19.83 Tf 0 0 Td[(a)]TJ/F15 19.83 Tf 15.87 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(N)]TJ ET 66.35 -6.97 0.6 23.91 re f 1 0 0 1 74.61 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(19)]TJ ET 32.46 -6.97 0.6 23.91 re f -405.06 -7.57 437.82 0.6 re f 1 0 0 1 -395 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.45 -6.97 0.6 23.91 re f 1 0 0 1 44.12 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 49.82 0 cm BT /F15 19.83 Tf 0 0 Td[(5040)]TJ ET 57.26 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.97 0.6 23.91 re f 1 0 0 1 40.74 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -411.26 -7.57 437.82 0.6 re f 1 0 0 1 -403.29 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(D)]TJ ET 25.54 -6.97 0.6 23.91 re f 1 0 0 1 46.21 0 cm BT /F15 19.83 Tf 0 0 Td[(91)]TJ ET 32.46 -6.97 0.6 23.91 re f 1 0 0 1 49.82 0 cm BT /F15 19.83 Tf 0 0 Td[(5120)]TJ ET 57.26 -6.97 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.27 -6.97 0.6 23.91 re f 1 0 0 1 40.74 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.97 0.6 23.91 re f -411.26 -7.57 437.82 0.6 re f 1 0 0 1 -401.68 -24.5 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ ET 23.93 -6.98 0.6 23.91 re f 1 0 0 1 32.2 0 cm BT /F15 19.83 Tf 0 0 Td[(171)]TJ ET 44.86 -6.98 0.6 23.91 re f 1 0 0 1 62.22 0 cm BT /F15 19.83 Tf 0 0 Td[(5200)]TJ ET 57.26 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.27 -6.98 0.6 23.91 re f 1 0 0 1 40.74 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f -411.26 -7.57 437.82 0.6 re f 1 0 0 1 -401.84 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(G)]TJ ET 24.09 -6.98 0.6 23.91 re f 1 0 0 1 32.36 0 cm BT /F15 19.83 Tf 0 0 Td[(196)]TJ ET 44.86 -6.98 0.6 23.91 re f 1 0 0 1 62.22 0 cm BT /F15 19.83 Tf 0 0 Td[(5225)]TJ ET 57.26 -6.98 0.6 23.91 re f 1 0 0 1 65.52 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 34.53 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.27 -6.98 0.6 23.91 re f 1 0 0 1 40.74 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 26.26 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 26.26 -6.98 0.6 23.91 re f -411.26 -7.57 437.82 0.6 re f 1 0 0 1 -425.97 -61.36 cm BT /F15 19.83 Tf 0 0 Td[(No)35(w)-417(compute)-417(over)]TJ/F34 20.66 Tf 199.29 0 Td[(Z)]TJ/F15 19.83 Tf 14.2 0 Td[(,)-417(not)-417(mo)-36(d)-416(2:)]TJ ET 33.51 -43.04 0.6 23.91 re f 1 0 0 1 41.78 -36.06 cm BT /F19 19.83 Tf 0 0 Td[(a=)]TJ/F15 19.83 Tf 21.73 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(a)]TJ/F15 19.83 Tf 15.87 0 Td[(+)]TJ/F19 19.83 Tf 23.97 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051)]TJ ET 107.36 -6.98 0.6 23.91 re f 1 0 0 1 144.41 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(3)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(5)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(7)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 32.33 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(13)]TJ ET 32.46 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(17)]TJ ET 32.47 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(19)]TJ ET 32.46 -6.98 0.6 23.91 re f -482.88 -7.58 515.64 0.6 re f 1 0 0 1 -472.82 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(A)]TJ ET 23.45 -6.98 0.6 23.91 re f 1 0 0 1 46.5 0 cm BT /F15 19.83 Tf 0 0 Td[(11)]TJ/F19 19.83 Tf 24.79 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(5040)]TJ ET 92.58 -6.98 0.6 23.91 re f 1 0 0 1 113.24 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(4)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(2)]TJ ET 36.45 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.45 -6.98 0.6 23.91 re f 1 0 0 1 61.11 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f -495.27 -7.57 515.64 0.6 re f 1 0 0 1 -487.3 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(D)]TJ ET 25.54 -6.97 0.6 23.91 re f 1 0 0 1 48.59 0 cm BT /F15 19.83 Tf 0 0 Td[(91)]TJ/F19 19.83 Tf 24.79 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(5120)]TJ ET 92.58 -6.97 0.6 23.91 re f 1 0 0 1 100.85 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(10)]TJ ET 48.85 -6.97 0.6 23.91 re f 1 0 0 1 73.51 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 61.12 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f -495.27 -7.57 515.64 0.6 re f 1 0 0 1 -485.69 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(F)]TJ ET 23.93 -6.97 0.6 23.91 re f 1 0 0 1 34.58 0 cm BT /F15 19.83 Tf 0 0 Td[(171)]TJ/F19 19.83 Tf 37.19 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(5200)]TJ ET 104.98 -6.97 0.6 23.91 re f 1 0 0 1 125.64 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(4)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 61.12 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(2)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 61.12 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.34 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.45 -6.97 0.6 23.91 re f 1 0 0 1 57.12 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(1)]TJ ET 20.07 -6.97 0.6 23.91 re f -495.27 -7.57 515.64 0.6 re f 1 0 0 1 -485.85 -24.51 cm BT /F19 19.83 Tf 0 0 Td[(G)]TJ ET 24.09 -6.97 0.6 23.91 re f 1 0 0 1 34.74 0 cm BT /F15 19.83 Tf 0 0 Td[(196)]TJ/F19 19.83 Tf 37.19 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(5225)]TJ ET 104.98 -6.97 0.6 23.91 re f 1 0 0 1 142.03 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(2)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 61.12 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f 1 0 0 1 61.12 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.97 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.97 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(1)]TJ ET 36.46 -6.97 0.6 23.91 re f -478.88 -7.57 515.64 0.6 re f -445.37 -31.48 0.6 23.91 re f -329.74 -31.48 0.6 23.91 re f -272.62 -31.48 0.6 23.91 re f -227.9 -31.48 0.6 23.91 re f -183.17 -31.48 0.6 23.91 re f -138.45 -31.48 0.6 23.91 re f -93.72 -31.48 0.6 23.91 re f -49 -31.48 0.6 23.91 re f -8.26 -31.48 0.6 23.91 re f 36.46 -31.48 0.6 23.91 re f -445.37 -55.39 0.6 23.91 re f 1 0 0 1 -380.53 -48.41 cm BT /F19 19.83 Tf 0 0 Td[(total)]TJ ET 50.79 -6.98 0.6 23.91 re f 1 0 0 1 59.06 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(16)]TJ ET 48.85 -6.98 0.6 23.91 re f 1 0 0 1 73.51 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 28.33 0 cm BT /F22 19.83 Tf 0 0 Td[( )]TJ/F15 19.83 Tf 16.39 0 Td[(6)]TJ ET 36.46 -6.98 0.6 23.91 re f 1 0 0 1 61.12 0 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.06 -6.98 0.6 23.91 re f 1 0 0 1 40.73 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f 1 0 0 1 44.72 0 cm BT /F15 19.83 Tf 0 0 Td[(0)]TJ ET 20.07 -6.98 0.6 23.91 re f -495.27 -7.58 515.64 0.6 re f 1 0 0 1 -495.27 -65.09 cm BT /F15 19.83 Tf 0 0 Td[(F)35(o)34(r)]TJ/F19 19.83 Tf 42.28 0 Td[(x)]TJ/F15 19.83 Tf 17.71 0 Td[(=)-296(7)]TJ/F19 19.83 Tf 37.53 0 Td[(;)-177(y)]TJ/F15 19.83 Tf 26.35 0 Td[(=)-296(2)]TJ/F17 16.53 Tf 37.53 7 Td[(8)]TJ/F15 19.83 Tf 10.83 -7 Td[(5)]TJ/F17 16.53 Tf 12.39 7 Td[(3)]TJ/F15 19.83 Tf 16.69 -7 Td[(=)-295(32000,)]TJ/F19 19.83 Tf 118.78 0 Td[(x)]TJ/F17 16.53 Tf 11.87 7 Td[(2)]TJ/F22 19.83 Tf 16.68 -7 Td[()]TJ/F19 19.83 Tf 22.24 0 Td[(y)]TJ/F17 16.53 Tf 11.13 7 Td[(2)]TJ/F15 19.83 Tf 19.09 -7 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(N)]TJ/F15 19.83 Tf 18.84 0 Td[(\051.)]TJ -429.58 -55.36 Td[(Ho)-34(o)34(ra)35(y!)-555(GCD\050N,)-417(32007\051)-418(=)-417(47.)]TJ ET endstream endobj 129 0 obj 11790 endobj 126 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F34 83 0 R /F22 13 0 R /F17 5 0 R >> /ProcSet [/PDF /Text] >> endobj 127 0 obj << /Type /Page /Contents 128 0 R /Resources 126 0 R /MediaBox [0 0 595.27 841.89] /Parent 113 0 R >> endobj 132 0 obj << /Length 133 0 R >> stream 1 0 0 1 165.83 697.48 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(P)35(erfo)36(rmance)]TJ -93.45 -57.78 Td[(Ho)35(w)-417(common)-417(a)34(re)-416(smo)-35(oth)-418(numb)-35(ers?)]TJ 0 -57.78 Td[(F)35(rom)-278(a)-278(random)-279(sample)-278(of)-278(integers)-277(of)-278(size)]TJ/F19 19.83 Tf 411.32 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-36(;)-177()]TJ/F15 19.83 Tf 32.63 0 Td[(],)]TJ -465.27 -27.9 Td[(the)-417(fraction)-417(of)]TJ/F19 19.83 Tf 154.94 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.7 0 Td[(])-417(smo)-35(oth)-418(ones)-416(is:)]TJ -106.44 -42.84 Td[(\011\050)]TJ/F19 19.83 Tf 28.92 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-36(;)-178()]TJ/F15 19.83 Tf 32.63 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(;)-177(L)]TJ/F15 19.83 Tf 23.69 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-27(;)-177()]TJ/F15 19.83 Tf 37.7 0 Td[(]\051)]TJ/F19 19.83 Tf 16.63 0 Td[(=L)]TJ/F15 19.83 Tf 24.87 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-36(;)-178()]TJ/F15 19.83 Tf 32.63 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -353.87 -67.74 Td[(The)-499(exp)-34(ected)-500(sample)-500(size)-500(to)-500(\014nd)-500(one)]TJ/F19 19.83 Tf 401.23 0 Td[(L)]TJ/F15 19.83 Tf 14.34 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.69 0 Td[(])]TJ -460.25 -27.9 Td[(smo)-35(oth)-418(ones)-416(is:)]TJ/F19 19.83 Tf 97.88 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-36(;)-177()]TJ/F15 19.83 Tf 32.63 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(\011\050)]TJ/F19 19.83 Tf 28.92 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)-37(;)-177()]TJ/F15 19.83 Tf 32.63 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(;)-177(L)]TJ/F15 19.83 Tf 23.7 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.7 0 Td[(]\051)-296(=)]TJ/F19 19.83 Tf -195.52 -47.82 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)]TJ/F22 19.83 Tf 15.65 0 Td[( )]TJ/F19 19.83 Tf 21.08 0 Td[(w)-26(;)]TJ/F15 19.83 Tf 25.02 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(v)]TJ/F22 19.83 Tf 15.65 0 Td[( )]TJ/F19 19.83 Tf 21.08 0 Td[(w)]TJ/F15 19.83 Tf 15.65 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(=)]TJ/F15 19.83 Tf 35.51 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -329.31 -67.74 Td[(The)-277(exp)-34(ected)-278(sample)-278(size)-278(to)-278(\014nd)]TJ/F19 19.83 Tf 329.09 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-27(;)-177()]TJ/F15 19.83 Tf 37.7 0 Td[(])-278(smo)-36(oth)]TJ -388.11 -27.9 Td[(ones)-417(is:)]TJ/F19 19.83 Tf 99.08 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.69 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(v)]TJ/F22 19.83 Tf 15.66 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)-26(;)]TJ/F15 19.83 Tf 25.02 0 Td[(\050)]TJ/F19 19.83 Tf 9.64 0 Td[(v)]TJ/F22 19.83 Tf 15.66 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)]TJ/F15 19.83 Tf 15.65 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(=)]TJ/F15 19.83 Tf 35.51 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ ET endstream endobj 133 0 obj 3187 endobj 130 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 131 0 obj << /Type /Page /Contents 132 0 R /Resources 130 0 R /MediaBox [0 0 595.27 841.89] /Parent 113 0 R >> endobj 136 0 obj << /Length 137 0 R >> stream 1 0 0 1 165.83 664.33 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(P)35(erfo)36(rmance)]TJ -93.45 -57.78 Td[(W)35(e)-277(cho)-35(ose)-278(a)-278(small)-278(p)34(rime)-277(b)-35(ound)]TJ/F19 19.83 Tf 317.32 0 Td[(B)]TJ/F15 19.83 Tf 22.38 0 Td[(of)-278(size)]TJ/F19 19.83 Tf 67.69 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-27(;)-177()]TJ/F15 19.83 Tf 37.7 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -473.4 -57.78 Td[(F)35(acto)34(r)-416(base)]TJ/F22 19.83 Tf 126.84 0 Td[(B)]TJ/F15 19.83 Tf 22.58 0 Td[(has)-417(size)]TJ/F19 19.83 Tf 86.83 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-27(;)-177()]TJ/F15 19.83 Tf 37.7 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -302.26 -57.79 Td[(Sea)35(rch)-416(fo)35(r)-417(smo)-35(oth)-417(pairs)]TJ/F19 19.83 Tf 251.07 0 Td[(a;)-178(N)]TJ/F15 19.83 Tf 44.08 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(a)]TJ/F15 19.83 Tf 11.2 0 Td[(;)]TJ/F19 19.83 Tf -330.31 -27.89 Td[(a)]TJ/F15 19.83 Tf 19.45 0 Td[(is)]TJ/F19 19.83 Tf 23.28 0 Td[(B)]TJ/F15 19.83 Tf 16.87 0 Td[(-smo)-35(oth.)]TJ/F19 19.83 Tf 101.78 0 Td[(N)]TJ/F15 19.83 Tf 23.52 0 Td[(+)]TJ/F19 19.83 Tf 23.96 0 Td[(a)]TJ/F15 19.83 Tf 19.46 0 Td[(has)-417(size)]TJ/F19 19.83 Tf 86.84 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([1)]TJ/F19 19.83 Tf 19.38 0 Td[(;)]TJ/F15 19.83 Tf 9.37 0 Td[(1].)]TJ -358.24 -57.79 Td[(Sea)35(rch)-416(region)-416(size:)]TJ/F19 19.83 Tf 103.8 -42.83 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([1)]TJ/F22 19.83 Tf 24.07 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)-26(;)]TJ/F15 19.83 Tf 25.02 0 Td[(\0501)]TJ/F22 19.83 Tf 26.72 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)]TJ/F15 19.83 Tf 15.66 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(=)]TJ/F15 19.83 Tf 23.21 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.7 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -357.59 -67.75 Td[(Linea)35(r)-417(algeb)35(ra)-417(p)35(roblem:)]TJ/F19 19.83 Tf 137.58 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.7 0 Td[(])]TJ/F17 16.53 Tf 6.99 8.24 Td[(2)]TJ/F15 19.83 Tf 16.68 -8.24 Td[(=)]TJ/F19 19.83 Tf 25.13 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-27(;)]TJ/F15 19.83 Tf 25.02 0 Td[(2)]TJ/F19 19.83 Tf 12.4 0 Td[()]TJ/F15 19.83 Tf 12.68 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ ET endstream endobj 137 0 obj 2424 endobj 134 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R /F17 5 0 R >> /ProcSet [/PDF /Text] >> endobj 135 0 obj << /Type /Page /Contents 136 0 R /Resources 134 0 R /MediaBox [0 0 595.27 841.89] /Parent 138 0 R >> endobj 141 0 obj << /Length 142 0 R >> stream 1 0 0 1 165.83 689.85 cm BT /F15 19.83 Tf 0 0 Td[(Rational)-418(Sieve)-415(P)35(erfo)36(rmance)]TJ -93.45 -57.79 Td[(Sea)35(rch)-416(region)-416(size:)]TJ/F19 19.83 Tf 103.8 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([1)]TJ/F22 19.83 Tf 24.07 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)-26(;)]TJ/F15 19.83 Tf 25.02 0 Td[(\0501)]TJ/F22 19.83 Tf 26.72 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)]TJ/F15 19.83 Tf 15.66 0 Td[(\051)]TJ/F19 19.83 Tf 9.64 0 Td[(=)]TJ/F15 19.83 Tf 23.21 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([)]TJ/F19 19.83 Tf 6.99 0 Td[(w)-26(;)-178()]TJ/F15 19.83 Tf 37.7 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -357.59 -67.74 Td[(Minimize)-416(max\050)]TJ/F19 19.83 Tf 150.05 0 Td[(w)-26(;)]TJ/F15 19.83 Tf 25.02 0 Td[(1)]TJ/F22 19.83 Tf 17.08 0 Td[( )]TJ/F19 19.83 Tf 21.07 0 Td[(w)]TJ/F15 19.83 Tf 15.66 0 Td[(\051:)]TJ/F19 19.83 Tf 35.8 0 Td[(w)]TJ/F15 19.83 Tf 21.51 0 Td[(=)-296(1)]TJ/F19 19.83 Tf 37.53 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(2.)]TJ -334.26 -27.9 Td[(Sea)35(rch)-416(region)-416(size)-417(is:)]TJ/F19 19.83 Tf 149.53 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([1)]TJ/F19 19.83 Tf 19.38 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(2)]TJ/F19 19.83 Tf 12.39 0 Td[(;)-178()]TJ/F15 19.83 Tf 26.73 0 Td[(+)-236(1)]TJ/F19 19.83 Tf 36.36 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(2)]TJ/F19 19.83 Tf 12.39 0 Td[()]TJ/F15 19.83 Tf 12.68 0 Td[(])]TJ/F19 19.83 Tf 6.99 0 Td[(:)]TJ/F15 19.83 Tf -311.86 -67.74 Td[(Minimum)-417(at)]TJ/F19 19.83 Tf 131.8 0 Td[()]TJ/F15 19.83 Tf 18.53 0 Td[(=)]TJ/F22 19.83 Tf 25.14 16.44 Td[(p)]TJ ET 99.58 -290.41 12.4 0.89 re f 1 0 0 1 99.58 -306.85 cm BT /F15 19.83 Tf 0 0 Td[(2)]TJ/F19 19.83 Tf 12.39 0 Td[(=)]TJ/F15 19.83 Tf 10.54 0 Td[(2.)]TJ -215.96 -27.9 Td[(Sea)35(rch)-416(region)-416(size)-417(is:)]TJ/F19 19.83 Tf 179.21 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([1)]TJ/F19 19.83 Tf 19.39 0 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(2)]TJ/F19 19.83 Tf 12.4 0 Td[(;)]TJ/F22 19.83 Tf 9.37 17.43 Td[(p)]TJ ET 69.76 -53.31 12.4 0.89 re f 1 0 0 1 69.76 -70.74 cm BT /F15 19.83 Tf 0 0 Td[(2])]TJ/F19 19.83 Tf 19.38 0 Td[(:)]TJ/F15 19.83 Tf -282.17 -67.74 Td[(Linea)35(r)-417(algeb)35(ra)-417(is)-417(also)]TJ/F19 19.83 Tf 179.21 -42.84 Td[(L)]TJ/F15 19.83 Tf 14.33 0 Td[([1)]TJ/F19 19.83 Tf 19.39 0 Td[(=)]TJ/F15 19.83 Tf 10.53 0 Td[(2)]TJ/F19 19.83 Tf 12.4 0 Td[(;)]TJ/F22 19.83 Tf 9.37 17.42 Td[(p)]TJ ET 0 -93.16 12.4 0.89 re f 1 0 0 1 0 -110.58 cm BT /F15 19.83 Tf 0 0 Td[(2])]TJ/F19 19.83 Tf 19.38 0 Td[(:)]TJ ET endstream endobj 142 0 obj 2496 endobj 139 0 obj << /Font << /F15 5 0 R /F19 12 0 R /F22 13 0 R >> /ProcSet [/PDF /Text] >> endobj 140 0 obj << /Type /Page /Contents 141 0 R /Resources 139 0 R /MediaBox [0 0 595.27 841.89] /Parent 138 0 R >> endobj 83 0 obj << /Type /Font /Subtype /Type1 /FirstChar 90 /LastChar 90 /Widths 143 0 R /BaseFont 149 0 R /FontDescriptor 150 0 R >> endobj 143 0 obj [ 688 ] endobj 144 0 obj << /Length 145 0 R /Length1 146 0 R /Length2 147 0 R /Length3 148 0 R >> stream %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /PDAAAA+CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 90 /Z put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec oc;j~EЪ*BgNӽؑlKq*Xws|QFqv`zXMyp"5O˩YŝP(DT! [v67XFlU&3!Rq4wσ~j+ou_dV`Ky Z]uMYb[1[l',t\pڮԞZO4GJ7 i!U &Ϸݢh`ZṆhKGz; #1&()$J3KُօEsjFf"P$-I˕B 6=hqDV<` EkENrraƌJG ~L{6IE6U'y 0gK>&)o>2\U]$XW-1f@'B1mW=L%5t.O-]NCT4>&wvNXŅC f עr1fׁVCȖ~q0Xf^^$ӷ%G7dȱ\lFc0]g<銷_&W{>}N|ӷ 054H4ܞlG>T_cќ6Y1 nUr-u$yfOσ4nA yغINz +:Џ}=|z`v+D{.;F WLEc6o, e&ۺH %&e+ o= 'a9ܮ;-sg}l3K?SEhAr;}5٠땷7_KߔZn+Kw$ZdvԬ|d-?n࣯Us;vmΓŵց|C䝅ںL i& i5u ͅRn\w4NNNihmfGxWf=6:eNBuNVǚiK2|c铜hc?46 VK= Ol0)մ|ΖA麂{E{ӤBkdl0wnN^6\`kӼm>511UFv >[/*0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark endstream endobj 145 0 obj 2427 endobj 146 0 obj 759 endobj 147 0 obj 1136 endobj 148 0 obj 532 endobj 149 0 obj /PDAAAA+CMBX12 endobj 150 0 obj << /Ascent 695 /CapHeight 686 /Descent -194 /FontName 149 0 R /ItalicAngle 0 /StemV 109 /XHeight 444 /FontBBox [ -53 -251 1139 750 ] /Flags 000004 /CharSet (/Z) /FontFile 144 0 R >> endobj 45 0 obj << /Type /Font /Subtype /Type1 /FirstChar 89 /LastChar 89 /Widths 151 0 R /BaseFont 157 0 R /FontDescriptor 158 0 R >> endobj 151 0 obj [ 1277 ] endobj 152 0 obj << /Length 153 0 R /Length1 154 0 R /Length2 155 0 R /Length3 156 0 R >> stream %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /ODAAAA+CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 89 /productdisplay put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec oc;j~EЪ*BgNӽؑlKq*Xws|QFqv`zXMyp"5O˩YŝP(DT! [v67XFlU&3!Rq4wσ~j+ou\Ƨ"v*o$1|#`ݧ2YȎK@瘉!QgDVWܑ>{03{iEmW~?B(403"Ԇ9NLJG9LNIWnNRY[dm+IfN|=cG5yJi,dRht x<#^!V&1qE1[nض{3#a#!LLk-(PAh1IvYK1[VYѲY*a FnH DhPPtHH'Í=(ճAf(8JH:cX~ ۘzkcF8!hG"Vpלwp_>#5J *fvb I3YeAIȪ]%RdxL > Z47וwqc>y66| ` - E>`P5@Xmx1b@CDDx3rtK0n#5~@ rS&`YCl!;Tߞ{>MX"_|#xw{UJC31I ͜pKe #tX?TvnOBePJnE\dggѢAT_NG?z2?3m6t_47&C0mڸc،ld0Doj3Џ] J eWsɓ*?JkB=qW&=rrS<^Y\, MҢW6E`&ڼ uЈg+/+W&,TY|tRIppmn\g/8j@Jdu$s[ M-t'y}R0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark endstream endobj 153 0 obj 2401 endobj 154 0 obj 777 endobj 155 0 obj 1092 endobj 156 0 obj 532 endobj 157 0 obj /ODAAAA+CMEX10 endobj 158 0 obj << /Ascent 40 /CapHeight 0 /Descent -1760 /FontName 157 0 R /ItalicAngle 0 /StemV 47 /XHeight 430 /FontBBox [ -24 -2960 1454 772 ] /Flags 000004 /CharSet (/productdisplay) /FontFile 152 0 R >> endobj 44 0 obj << /Type /Font /Subtype /Type1 /FirstChar 12 /LastChar 125 /Widths 159 0 R /BaseFont 165 0 R /FontDescriptor 166 0 R >> endobj 159 0 obj [ 722 722 1104 1104 299 337 688 688 688 688 688 889 611 646 993 1070 688 1170 1323 1070 299 392 688 1146 688 1183 1028 382 535 535 688 1070 382 458 382 688 688 688 688 688 688 688 688 688 688 688 382 382 392 1070 649 649 917 889 903 879 979 854 816 917 899 361 636 927 778 1129 899 1059 865 1059 898 764 983 894 889 1271 889 889 840 417 688 417 688 382 382 646 681 611 681 627 420 681 681 299 337 642 299 1063 681 688 681 681 455 527 497 681 604 910 604 604 590 688 1375 688 ] endobj 160 0 obj << /Length 161 0 R /Length1 162 0 R /Length2 163 0 R /Length3 164 0 R >> stream %!PS-AdobeFont-1.1: LCMSSB8 1.01 %%CreationDate: 1992 Jun 07 22:46:27 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.01) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved.) readonly def /FullName (LCMSSB8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /EMILLW+LCMSSB8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /fi put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 45 /hyphen put dup 67 /C put dup 69 /E put dup 70 /F put dup 76 /L put dup 78 /N put dup 80 /P put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 125 /hungarumlaut put readonly def /FontBBox{-99 -209 1413 840}readonly def /UniqueID 5029035 def currentdict end currentfile eexec oc;j~EЪ*BgNӽؑlKq*Xws|QFqv`zXMyp"5O˩YŝP(DT! [v67XFlU&3!Rq4wσ~j+ou\@[|Qŋ h낱}IlC=h{Wd_jռТ'Z@j9% `;wSA_CAY[Q|̀Am{)ݐ;øVe0/3%fw+F3pNR6> nGLkkT&`-L<9T|kc)>.r;uҢC8Tf+.751fōa~cEe9"QcF%)?#>&wߓe'7p=Rc-+Bq>%Ъd1c$=WT4{,%9+5k+!-xE/@mo AO5ncS o~ˀTiVt@n,n=岤`0j ;W[>!V˷XeX?4J@9`Ȥ+G#1U䠃h(\q$#̝x1dCC(KH" MFf{aih3 K_ JЏeecLp u/-E|e M ӔdںNq|sD,XgWI2Ԟ7s4ƉE.8 /6unQGSX9}RCo(C=op33_ȣaפnsqAjͦ6dt33piC<6%"O/q:^wMJT! jnALC,)0I3c[:> !,#1 E