%PDF-1.2 3 0 obj << /Length 4 0 R >> stream 1 0 0 1 157.38 724.12 cm BT /F39 11.96 Tf 0 0 Td[(Robin)-375(Hartshorne's)-375(Algebraic)-376(Geometry)-375(Solutions)]TJ/F15 10.91 Tf 108.76 -16.12 Td[(b)29(y)-333(Jinh)29(yun)-332(P)27(ark)]TJ/F40 10.91 Tf -59 -30.3 Td[(Appendix)-378(C;)-378(The)-378(Weil)-378(Conjectures)]TJ/F38 10.91 Tf -117.14 -19.42 Td[(Exercise)-383(5.1.)]TJ/F15 10.91 Tf 74.69 0 Td[(Let)]TJ/F42 10.91 Tf 19.55 0 Td[(X)]TJ/F15 10.91 Tf 12.92 0 Td[(=)]TJ/F46 10.91 Tf 11.51 8.18 Td[(`)]TJ/F43 7.97 Tf 10.31 -11.41 Td[(i)]TJ/F42 10.91 Tf 5.2 3.23 Td[(X)]TJ/F43 7.97 Tf 9.03 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.39 1.64 Td[(.)-444(Ob)29(viously)84(,)-333(then,)]TJ/F42 10.91 Tf 89.15 0 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(r)]TJ/F15 10.91 Tf 4.56 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)]TJ/F15 10.91 Tf 9.89 0 Td[(\051)-278(=)]TJ/F46 10.91 Tf 18.79 8.18 Td[(P)]TJ/F43 7.97 Tf 11.52 -11.41 Td[(i)]TJ/F42 10.91 Tf 5.2 3.23 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(r)]TJ/F15 10.91 Tf 4.56 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)]TJ/F43 7.97 Tf 9.04 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.38 1.64 Td[(\051)-333(so)-334(that)]TJ/F42 10.91 Tf -239.99 -28.72 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)-23(;)-167(t)]TJ/F15 10.91 Tf 18.07 0 Td[(\051)-278(=)-277(exp\050)]TJ/F45 7.97 Tf 43.35 13.63 Td[(1)]TJ/F46 10.91 Tf -3.65 -3.27 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F42 10.91 Tf 13.08 12.96 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(r)]TJ/F15 10.91 Tf 4.56 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)]TJ/F15 10.91 Tf 9.89 0 Td[(\051)]TJ/F42 10.91 Tf 5.44 7.38 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET 142.03 -92.05 8.49 0.44 re f 1 0 0 1 143.66 -102.05 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.06 7.49 Td[(\051)-278(=)-277(exp\050)]TJ/F45 7.97 Tf 43.34 13.63 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.27 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.05 0 Td[(=1)]TJ/F46 10.91 Tf 13.08 23.32 Td[(X)]TJ/F43 7.97 Tf 6.44 -23.45 Td[(i)]TJ/F42 10.91 Tf 11.14 13.09 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(r)]TJ/F15 10.91 Tf 4.56 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)]TJ/F43 7.97 Tf 9.04 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.38 1.64 Td[(\051)]TJ/F42 10.91 Tf 5.44 7.38 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET 118.33 10 8.49 0.44 re f 1 0 0 1 119.96 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.06 7.49 Td[(\051)]TJ -276.22 -41.48 Td[(=)-277(exp\050)]TJ/F46 10.91 Tf 32.42 10.36 Td[(X)]TJ/F43 7.97 Tf 6.44 -23.45 Td[(i)]TJ/F45 7.97 Tf 14.78 26.73 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.28 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.31 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F42 10.91 Tf 13.08 12.95 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(r)]TJ/F15 10.91 Tf 4.56 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)]TJ/F43 7.97 Tf 9.04 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.38 1.64 Td[(\051)]TJ/F42 10.91 Tf 5.43 7.38 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET -165.17 -31.48 8.49 0.44 re f 1 0 0 1 -163.53 -41.47 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.05 7.48 Td[(\051)-278(=)]TJ/F46 10.91 Tf 18.79 10.36 Td[(Y)]TJ/F43 7.97 Tf 5.53 -23.45 Td[(i)]TJ/F15 10.91 Tf 10.23 13.09 Td[(exp\050)]TJ/F45 7.97 Tf 24.55 13.64 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.28 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.31 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F42 10.91 Tf 13.07 12.95 Td[(N)]TJ/F43 7.97 Tf 8.77 -1.64 Td[(r)]TJ/F15 10.91 Tf 4.55 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(X)]TJ/F43 7.97 Tf 9.03 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.39 1.64 Td[(\051)]TJ/F42 10.91 Tf 5.43 7.38 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET 116.5 9.99 8.49 0.44 re f 1 0 0 1 118.14 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.05 7.48 Td[(\051)-278(=)]TJ/F46 10.91 Tf 18.79 10.36 Td[(Y)]TJ/F43 7.97 Tf 5.53 -23.45 Td[(i)]TJ/F42 10.91 Tf 10.23 13.09 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)]TJ/F43 7.97 Tf 9.04 -1.64 Td[(i)]TJ/F42 10.91 Tf 3.38 1.64 Td[(;)-166(t)]TJ/F15 10.91 Tf 8.79 0 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F38 10.91 Tf -366.13 -32.84 Td[(Exercise)-491(5.2.)]TJ/F15 10.91 Tf 75.87 0 Td[(The)-427(p)-27(oin)28(t)-427(is)-427(to)-427(compute)-428(the)-427(n)29(um)28(b)-28(er)-427(of)]TJ/F42 10.91 Tf 198.59 0 Td[(k)]TJ/F43 7.97 Tf 5.68 -1.63 Td[(r)]TJ/F15 10.91 Tf 9.29 1.63 Td[(=)]TJ/F50 10.91 Tf 13.22 0 Td[(F)]TJ/F43 7.97 Tf 6.67 -1.63 Td[(q)]TJ/F26 5.98 Tf 4.07 2.27 Td[(r)]TJ/F15 10.91 Tf 4.65 -0.64 Td[(-rational)-426(p)-27(oin)28(ts,)-451(i.e.)-725(to)]TJ -318.04 -13.13 Td[(compute)]TJ/F42 10.91 Tf 44.24 0 Td[(N)]TJ/F43 7.97 Tf 8.77 -1.64 Td[(r)]TJ/F15 10.91 Tf 8.19 1.64 Td[(in)]TJ 15.85 2.76 Td[()]TJ/F42 10.91 Tf -3.12 -2.76 Td[(X)]TJ/F15 10.91 Tf 12.92 0 Td[(=)]TJ/F50 10.91 Tf 11.51 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F41 7.97 Tf 0.2 -6.32 Td[()]TJ/F43 7.97 Tf -0.2 -2.1 Td[(k)]TJ/F15 10.91 Tf 5.64 4.46 Td[(.)-444(W)84(e)-334(can)-333(consider)-333(the)-333(follo)29(wing)]TJ/F52 10.91 Tf 154.03 0 Td[(str)52(ati\014c)51(ation)]TJ/F15 10.91 Tf 63.15 0 Td[(of)]TJ/F50 10.91 Tf 12.43 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F15 10.91 Tf 5.63 -3.96 Td[(:)]TJ/F50 10.91 Tf -260.83 -21.44 Td[(P)]TJ/F43 7.97 Tf 6.67 4.51 Td[(n)]TJ/F15 10.91 Tf 8.67 -4.51 Td[(=)]TJ/F50 10.91 Tf 11.51 0 Td[(A)]TJ/F43 7.97 Tf 7.88 4.51 Td[(n)]TJ/F44 10.91 Tf 8.06 -4.51 Td[([)]TJ/F50 10.91 Tf 9.7 0 Td[(P)]TJ/F43 7.97 Tf 6.66 4.51 Td[(n)]TJ/F45 7.97 Tf 5.14 0 Td[( )]TJ/F41 7.97 Tf 6.59 0 Td[(1)]TJ/F15 10.91 Tf 7.76 -4.51 Td[(=)]TJ/F44 10.91 Tf 11.52 0 Td[()-166()-166()]TJ/F15 10.91 Tf 15.75 0 Td[(=)]TJ/F50 10.91 Tf 11.52 0 Td[(A)]TJ/F43 7.97 Tf 7.88 4.51 Td[(n)]TJ/F44 10.91 Tf 8.06 -4.51 Td[([)]TJ/F50 10.91 Tf 9.69 0 Td[(A)]TJ/F43 7.97 Tf 7.88 4.51 Td[(n)]TJ/F45 7.97 Tf 5.14 0 Td[( )]TJ/F41 7.97 Tf 6.59 0 Td[(1)]TJ/F44 10.91 Tf 7.15 -4.51 Td[([)-222()-167()-166()-222([)]TJ/F50 10.91 Tf 34.55 0 Td[(A)]TJ/F41 7.97 Tf 7.88 4.51 Td[(1)]TJ/F44 10.91 Tf 7.15 -4.51 Td[([)-222(fg)]TJ/F42 10.91 Tf 26.07 0 Td[(:)]TJ/F15 10.91 Tf -337.22 -19.29 Td[(Hence)-334(for)-332(a)-334(\014eld)]TJ/F42 10.91 Tf 81.85 0 Td[(k)]TJ/F43 7.97 Tf 5.68 -1.63 Td[(r)]TJ/F15 10.91 Tf 8.19 1.63 Td[(of)]TJ/F42 10.91 Tf 12.42 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(r)]TJ/F15 10.91 Tf 8.19 -3.96 Td[(elemen)27(ts,)]TJ/F50 10.91 Tf 47.64 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ 0 -7.28 Td[(k)]TJ/F26 5.98 Tf 4.41 -0.99 Td[(r)]TJ/F15 10.91 Tf 8.29 4.31 Td[(has)]TJ/F42 10.91 Tf 19.45 0 Td[(N)]TJ/F43 7.97 Tf 8.77 -1.63 Td[(r)]TJ/F15 10.91 Tf 7.58 1.63 Td[(=)-278(1)-222(+)]TJ/F42 10.91 Tf 30.31 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(r)]TJ/F15 10.91 Tf 6.98 -3.96 Td[(+)]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F41 7.97 Tf 5.26 3.96 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(r)]TJ/F15 10.91 Tf 6.98 -3.96 Td[(+)]TJ/F44 10.91 Tf 10.91 0 Td[()-166()-167()]TJ/F15 10.91 Tf 15.15 0 Td[(+)]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(nr)]TJ/F15 10.91 Tf 13.33 -3.96 Td[(p)-27(oin)28(ts.)-444(Hence,)]TJ/F42 10.91 Tf -283.41 -29.81 Td[(Z)]TJ/F15 10.91 Tf 8.22 0 Td[(\050)]TJ/F50 10.91 Tf 4.25 0 Td[(P)]TJ/F43 7.97 Tf 6.66 4.51 Td[(n)]TJ/F42 10.91 Tf 5.64 -4.51 Td[(;)-166(t)]TJ/F15 10.91 Tf 8.79 0 Td[(\051)-277(=)-278(exp\050)]TJ/F45 7.97 Tf 43.34 13.64 Td[(1)]TJ/F46 10.91 Tf -3.65 -3.27 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F44 10.91 Tf 11.26 12.95 Td[(f)]TJ/F15 10.91 Tf 5.46 0 Td[(1)-222(+)]TJ/F42 10.91 Tf 18.78 0 Td[(q)]TJ/F43 7.97 Tf 5.26 4.51 Td[(r)]TJ/F15 10.91 Tf 6.98 -4.51 Td[(+)]TJ/F44 10.91 Tf 10.91 0 Td[()-167()-166()]TJ/F15 10.91 Tf 15.15 0 Td[(+)]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 4.51 Td[(nr)]TJ/F44 10.91 Tf 9.7 -4.51 Td[(g)]TJ/F42 10.91 Tf 6.65 7.38 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET -35.06 -106.52 8.49 0.44 re f 1 0 0 1 -33.43 -116.51 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.06 7.48 Td[(\051)-277(=)]TJ/F43 7.97 Tf 23.19 13.64 Td[(n)]TJ/F46 10.91 Tf -4.41 -3.27 Td[(Y)]TJ/F43 7.97 Tf 0.12 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.89 0 Td[(=0)]TJ/F15 10.91 Tf 12.75 13.08 Td[(exp\050)]TJ/F45 7.97 Tf 24.56 13.64 Td[(1)]TJ/F46 10.91 Tf -3.65 -3.27 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F15 10.91 Tf 14.27 20.33 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(q)]TJ/F43 7.97 Tf 5.27 3.96 Td[(i)]TJ/F42 10.91 Tf 3.38 -3.96 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ/F43 7.97 Tf 4.24 3.96 Td[(r)]TJ ET 82.28 9.99 25.62 0.44 re f 1 0 0 1 92.48 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 16.62 7.48 Td[(\051)]TJ -308.71 -41.47 Td[(=)]TJ/F43 7.97 Tf 15.91 13.63 Td[(n)]TJ/F46 10.91 Tf -4.4 -3.27 Td[(Y)]TJ/F43 7.97 Tf 0.12 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=0)]TJ/F15 10.91 Tf 12.76 13.09 Td[(exp\050)]TJ/F44 10.91 Tf 20.91 0 Td[( )]TJ/F15 10.91 Tf 10.3 0 Td[(log)-14(\0501)]TJ/F44 10.91 Tf 26.21 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.27 4.5 Td[(i)]TJ/F42 10.91 Tf 3.38 -4.5 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\051)-277(=)]TJ/F43 7.97 Tf 27.43 13.63 Td[(n)]TJ/F46 10.91 Tf -4.4 -3.27 Td[(Y)]TJ/F43 7.97 Tf 0.11 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.89 0 Td[(=0)]TJ/F15 10.91 Tf 26.91 20.47 Td[(1)]TJ ET -143.92 -31.48 31.37 0.44 re f 1 0 0 1 -143.92 -41.48 cm BT /F15 10.91 Tf 0 0 Td[(1)]TJ/F44 10.91 Tf 7.88 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.16 Td[(i)]TJ/F42 10.91 Tf 3.38 -3.16 Td[(t)]TJ/F15 10.91 Tf 8.16 7.49 Td[(=)]TJ 73.07 7.38 Td[(1)]TJ ET 48.31 10 126.16 0.44 re f 1 0 0 1 48.31 0 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.93 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)-36(t)]TJ/F15 10.91 Tf 9.2 0 Td[(\051)]TJ/F44 10.91 Tf 6.06 0 Td[()-166()-167()]TJ/F15 10.91 Tf 14.54 0 Td[(\0501)]TJ/F44 10.91 Tf 12.13 0 Td[( )]TJ/F42 10.91 Tf 10.9 0 Td[(q)]TJ/F43 7.97 Tf 5.27 3.16 Td[(n)]TJ/F42 10.91 Tf 5.63 -3.16 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ/F42 10.91 Tf 5.44 7.49 Td[(:)]TJ/F15 10.91 Tf -364.45 -27.43 Td[(Ob)28(viously)85(,)-396(this)-384(is)-384(a)-383(rational)-382(function)-382(so)-384(that)-383(\0501.1\051)-383(is)-384(true.)-595(Also,)-396(w)28(e)-384(ha)28(v)28(e)]TJ/F42 10.91 Tf 357.38 0 Td[(P)]TJ/F15 10.91 Tf 7 -3.82 Td[(o)-28(dd)]TJ 18.38 3.82 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)-362(=)-361(1,)]TJ/F42 10.91 Tf -402.89 -16.33 Td[(P)]TJ/F41 7.97 Tf 7 -1.64 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(i)]TJ/F15 10.91 Tf 3.38 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)-278(=)-277(1)]TJ/F44 10.91 Tf 26.67 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.95 Td[(i)]TJ/F42 10.91 Tf 3.38 -3.95 Td[(t)]TJ/F15 10.91 Tf 7.57 0 Td[(so)-334(that)-333(\0501.3\051)-332(is)-334(true,)-332(b)-27(ecause)]TJ/F44 10.91 Tf 140.52 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.95 Td[(i)]TJ/F44 10.91 Tf 3.38 -3.95 Td[(j)]TJ/F15 10.91 Tf 6.06 0 Td[(=)]TJ/F42 10.91 Tf 11.52 0 Td[(q)]TJ/F24 5.98 Tf 6.45 7.55 Td[(2)]TJ/F26 5.98 Tf 3.66 0 Td[(i)]TJ ET 3.76 -30.16 6.32 0.36 re f 1 0 0 1 5.1 -35.1 cm BT /F24 5.98 Tf 0 0 Td[(2)]TJ/F15 10.91 Tf 6.67 -1.17 Td[(,)-333(indeed.)]TJ -248.87 -12.96 Td[(Let's)-372(\014nd)-369(the)-370(self)-371(in)29(tersection)-371(n)28(um)28(b)-27(er)]TJ/F42 10.91 Tf 187.39 0 Td[(E)]TJ/F15 10.91 Tf 12.73 0 Td[(of)-370()-371(in)]TJ/F50 10.91 Tf 39.1 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F44 10.91 Tf 8.33 -3.96 Td[()]TJ/F50 10.91 Tf 11.18 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F15 10.91 Tf 5.63 -3.96 Td[(.)-557(Note)-370(that)]TJ/F42 10.91 Tf 59.92 0 Td[(C)-71(H)]TJ/F45 7.97 Tf 18.53 3.96 Td[()]TJ/F15 10.91 Tf 4.74 -3.96 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.66 3.96 Td[(n)]TJ/F44 10.91 Tf 8.34 -3.96 Td[()]TJ/F50 10.91 Tf 11.18 0 Td[(P)]TJ/F43 7.97 Tf 6.66 3.96 Td[(n)]TJ/F15 10.91 Tf 5.64 -3.96 Td[(\051)]TJ/F44 10.91 Tf 7.95 0 Td[(')]TJ/F42 10.91 Tf -423.51 -12.95 Td[(C)-71(H)]TJ/F45 7.97 Tf 18.53 3.96 Td[()]TJ/F15 10.91 Tf 4.73 -3.96 Td[(\050)]TJ/F50 10.91 Tf 4.25 0 Td[(P)]TJ/F43 7.97 Tf 6.66 3.96 Td[(n)]TJ/F15 10.91 Tf 5.64 -3.96 Td[(\051)]TJ/F44 10.91 Tf 6.67 0 Td[(\012)]TJ/F42 10.91 Tf 10.9 0 Td[(C)-72(H)]TJ/F45 7.97 Tf 18.54 3.96 Td[()]TJ/F15 10.91 Tf 4.73 -3.96 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F15 10.91 Tf 5.63 -3.96 Td[(\051)-334(so)-333(that)-333(in)-332(particular,)-331(w)27(e)-333(ha)28(v)28(e)]TJ/F42 10.91 Tf 33.13 -19.83 Td[(C)-71(H)]TJ/F43 7.97 Tf 18.53 4.5 Td[(n)]TJ/F15 10.91 Tf 5.64 -4.5 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.67 4.5 Td[(n)]TJ/F44 10.91 Tf 8.06 -4.5 Td[()]TJ/F50 10.91 Tf 10.91 0 Td[(P)]TJ/F43 7.97 Tf 6.67 4.5 Td[(n)]TJ/F15 10.91 Tf 5.63 -4.5 Td[(\051)]TJ/F44 10.91 Tf 7.28 0 Td[(')-2596(\010)]TJ/F43 7.97 Tf 11.51 -8.06 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(+)]TJ/F43 7.97 Tf 6.59 0 Td[(j)]TJ/F41 7.97 Tf 3.88 0 Td[(=)]TJ/F43 7.97 Tf 6.59 0 Td[(n;)]TJ/F41 7.97 Tf 7.49 0 Td[(0)]TJ/F45 7.97 Tf 4.23 0 Td[()]TJ/F43 7.97 Tf 6.59 0 Td[(i;j)]TJ/F45 7.97 Tf 9.12 0 Td[()]TJ/F43 7.97 Tf 6.59 0 Td[(n)]TJ/F50 10.91 Tf 5.14 8.06 Td[(Z)]TJ/F42 10.91 Tf 7.27 0 Td[(s)]TJ/F43 7.97 Tf 5.11 4.5 Td[(i)]TJ/F42 10.91 Tf 3.38 -4.5 Td[(t)]TJ/F43 7.97 Tf 3.94 4.5 Td[(j)]TJ/F42 10.91 Tf 4.38 -4.5 Td[(;)]TJ/F15 10.91 Tf -298.64 -27.26 Td[(where)]TJ/F42 10.91 Tf 31.6 0 Td[(s)]TJ/F43 7.97 Tf 5.11 3.96 Td[(i)]TJ/F42 10.91 Tf 3.38 -3.96 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(j)]TJ/F15 10.91 Tf 8.07 -3.96 Td[(corresp)-28(onds)-338(to)-338(an)]TJ/F42 10.91 Tf 88.53 0 Td[(n)]TJ/F15 10.91 Tf 6.55 0 Td[(-cycle)]TJ/F50 10.91 Tf 30.66 0 Td[(P)]TJ/F43 7.97 Tf 6.66 3.96 Td[(i)]TJ/F44 10.91 Tf 5.84 -3.96 Td[()]TJ/F50 10.91 Tf 10.95 0 Td[(P)]TJ/F43 7.97 Tf 6.66 3.96 Td[(j)]TJ/F15 10.91 Tf 8.08 -3.96 Td[(in)]TJ/F50 10.91 Tf 12.78 0 Td[(P)]TJ/F43 7.97 Tf 6.66 3.96 Td[(n)]TJ/F44 10.91 Tf 8.1 -3.96 Td[()]TJ/F50 10.91 Tf 10.94 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F15 10.91 Tf 5.64 -3.96 Td[(.)-459(Hence)-338(if)-338()-286(=)]TJ/F46 10.91 Tf 74.38 8.18 Td[(P)]TJ/F43 7.97 Tf 11.52 -11.41 Td[(i;j)]TJ/F42 10.91 Tf 11.43 3.23 Td[(a)]TJ/F43 7.97 Tf 5.77 -1.64 Td[(ij)]TJ/F42 10.91 Tf 7.26 1.64 Td[(s)]TJ/F43 7.97 Tf 5.12 3.96 Td[(i)]TJ/F42 10.91 Tf 3.38 -3.96 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(j)]TJ/F15 10.91 Tf 4.38 -3.96 Td[(,)-339(then)-338(if)]TJ -394 -15.86 Td[(w)28(e)-324(lo)-28(ok)-323(at)-323(the)-324(in)29(tersection)-324(pro)-27(duct,)-324(\050)]TJ/F42 10.91 Tf 187.08 0 Td[(:)]TJ/F15 10.91 Tf 3.03 0 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.95 Td[(i)]TJ/F44 10.91 Tf 5.59 -3.95 Td[()]TJ/F50 10.91 Tf 10.69 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.95 Td[(j)]TJ/F15 10.91 Tf 4.38 -3.95 Td[(\051\051)-278(=)-277(1.)-441(Also,)-325(\050)]TJ/F42 10.91 Tf 68.12 0 Td[(s)]TJ/F43 7.97 Tf 5.12 3.95 Td[(i)]TJ/F42 10.91 Tf 3.38 -3.95 Td[(t)]TJ/F43 7.97 Tf 3.94 3.95 Td[(j)]TJ/F15 10.91 Tf 4.38 -3.95 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F15 10.91 Tf 3.03 0 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(s)]TJ/F43 7.97 Tf 5.11 3.95 Td[(i)]TJ/F28 5.98 Tf 2.88 2.82 Td[(0)]TJ/F42 10.91 Tf 3.19 -6.77 Td[(t)]TJ/F43 7.97 Tf 3.93 3.95 Td[(j)]TJ/F28 5.98 Tf 3.89 2.82 Td[(0)]TJ/F15 10.91 Tf 3.18 -6.77 Td[(\051)-278(=)-277(1)-324(i)]TJ/F42 10.91 Tf 40.7 0 Td[(i)]TJ/F15 10.91 Tf 5.97 0 Td[(+)]TJ/F42 10.91 Tf 10.69 0 Td[(i)]TJ/F45 7.97 Tf 3.76 3.95 Td[(0)]TJ/F15 10.91 Tf 5.83 -3.95 Td[(=)]TJ/F42 10.91 Tf 11.51 0 Td[(n)]TJ/F15 10.91 Tf -425.45 -12.96 Td[(and)]TJ/F42 10.91 Tf 21.21 0 Td[(j)]TJ/F15 10.91 Tf 7.54 0 Td[(+)]TJ/F42 10.91 Tf 10.91 0 Td[(j)]TJ/F45 7.97 Tf 5.12 3.96 Td[(0)]TJ/F15 10.91 Tf 5.82 -3.96 Td[(=)]TJ/F42 10.91 Tf 11.52 0 Td[(n)]TJ/F15 10.91 Tf 10.18 0 Td[(and)-333(otherwise)-333(it)-333(is)-333(0.)-444(Hence)-334(eac)27(h)]TJ/F42 10.91 Tf 161.97 0 Td[(a)]TJ/F43 7.97 Tf 5.77 -1.63 Td[(ij)]TJ/F15 10.91 Tf 10.29 1.63 Td[(=)-278(1.)-444(That)-333(is,)]TJ/F42 10.91 Tf -135.08 -21.97 Td[(E)]TJ/F15 10.91 Tf 11.71 0 Td[(=)-277(\050)]TJ/F42 10.91 Tf 24.85 0 Td[(:)]TJ/F15 10.91 Tf 3.03 0 Td[(\051)-278(=)-277(\050)]TJ/F46 10.91 Tf 32.12 10.36 Td[(X)]TJ/F43 7.97 Tf 3.32 -23.45 Td[(i;j)]TJ/F42 10.91 Tf 14.25 13.09 Td[(s)]TJ/F43 7.97 Tf 5.12 4.5 Td[(i)]TJ/F42 10.91 Tf 3.38 -4.5 Td[(t)]TJ/F43 7.97 Tf 3.94 4.5 Td[(j)]TJ/F15 10.91 Tf 4.38 -4.5 Td[(\051\050)]TJ/F46 10.91 Tf 8.49 10.36 Td[(X)]TJ/F43 7.97 Tf 0.63 -23.77 Td[(i)]TJ/F28 5.98 Tf 2.88 2.27 Td[(0)]TJ/F43 7.97 Tf 2.69 -2.27 Td[(;j)]TJ/F28 5.98 Tf 6.23 2.27 Td[(0)]TJ/F42 10.91 Tf 5.14 11.14 Td[(s)]TJ/F43 7.97 Tf 5.12 4.5 Td[(i)]TJ/F28 5.98 Tf 2.88 2.82 Td[(0)]TJ/F42 10.91 Tf 3.18 -7.32 Td[(t)]TJ/F43 7.97 Tf 3.94 4.5 Td[(j)]TJ/F28 5.98 Tf 3.88 2.82 Td[(0)]TJ/F15 10.91 Tf 3.19 -7.32 Td[(\051)-277(=)]TJ/F42 10.91 Tf 18.78 0 Td[(n)]TJ/F15 10.91 Tf 8.98 0 Td[(+)-222(1)]TJ/F42 10.91 Tf 16.36 0 Td[(:)]TJ/F15 10.91 Tf -301.77 -30.84 Td[(No)27(w,)]TJ/F42 10.91 Tf 18.54 -25.93 Td[(Z)]TJ/F15 10.91 Tf 8.22 0 Td[(\050)]TJ/F50 10.91 Tf 4.25 0 Td[(P)]TJ/F43 7.97 Tf 6.66 4.5 Td[(n)]TJ/F42 10.91 Tf 5.64 -4.5 Td[(;)]TJ/F15 10.91 Tf 10.73 7.38 Td[(1)]TJ ET -192.85 -179.22 14.84 0.44 re f 1 0 0 1 -192.85 -189.21 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(n)]TJ/F42 10.91 Tf 5.64 -3.15 Td[(t)]TJ/F15 10.91 Tf 5.14 7.48 Td[(\051)-277(=)]TJ 88.97 7.38 Td[(1)]TJ ET 36.02 9.99 143.44 0.44 re f 1 0 0 1 36.02 -0.75 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F41 7.97 Tf 16.1 4.29 Td[(1)]TJ ET 24.22 2.51 12.22 0.44 re f 1 0 0 1 24.22 -3.76 cm BT /F43 7.97 Tf 0 0 Td[(q)]TJ/F26 5.98 Tf 4.07 2.27 Td[(n)]TJ/F43 7.97 Tf 5.1 -2.27 Td[(t)]TJ/F15 10.91 Tf 4.25 3.76 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F41 7.97 Tf 20.8 4.29 Td[(1)]TJ ET 41.89 6.27 21.63 0.44 re f 1 0 0 1 41.89 -0.29 cm BT /F43 7.97 Tf 0 0 Td[(q)]TJ/F26 5.98 Tf 4.07 2.27 Td[(n)]TJ/F28 5.98 Tf 4.6 0 Td[( )]TJ/F24 5.98 Tf 5.76 0 Td[(1)]TJ/F43 7.97 Tf 4.15 -2.27 Td[(t)]TJ/F15 10.91 Tf 4.25 4.05 Td[(\051)]TJ/F44 10.91 Tf 6.06 0 Td[()-166()-167()]TJ/F15 10.91 Tf 14.55 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F41 7.97 Tf 12.1 4.29 Td[(1)]TJ ET 67.66 6.56 4.23 0.44 re f 1 0 0 1 68.25 0.29 cm BT /F43 7.97 Tf 0 0 Td[(t)]TJ/F15 10.91 Tf 4.84 3.76 Td[(\051)]TJ 8.47 8.23 Td[(=)]TJ 40.89 7.38 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(q)]TJ/F43 7.97 Tf 5.27 3.96 Td[(n)]TJ/F42 10.91 Tf 5.63 -3.96 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\050)]TJ/F42 10.91 Tf 8.49 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(n)]TJ/F45 7.97 Tf 5.14 0 Td[( )]TJ/F41 7.97 Tf 6.58 0 Td[(1)]TJ/F42 10.91 Tf 4.73 -3.96 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ/F44 10.91 Tf 6.06 0 Td[()-167()-166()]TJ/F15 10.91 Tf 14.55 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ ET 26.02 14.5 142.62 0.44 re f 1 0 0 1 26.02 4.51 cm BT /F15 10.91 Tf 0 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(n)]TJ/F42 10.91 Tf 5.64 -3.15 Td[(t)]TJ/F44 10.91 Tf 6.36 0 Td[( )]TJ/F15 10.91 Tf 10.91 0 Td[(1\051\050)]TJ/F42 10.91 Tf 13.94 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(n)]TJ/F45 7.97 Tf 5.14 0 Td[( )]TJ/F41 7.97 Tf 6.59 0 Td[(1)]TJ/F42 10.91 Tf 4.73 -3.15 Td[(t)]TJ/F44 10.91 Tf 6.36 0 Td[( )]TJ/F15 10.91 Tf 10.91 0 Td[(1\051)]TJ/F44 10.91 Tf 11.52 0 Td[()-166()-167()]TJ/F15 10.91 Tf 14.54 0 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(t)]TJ/F44 10.91 Tf 6.36 0 Td[( )]TJ/F15 10.91 Tf 10.91 0 Td[(1\051)]TJ -325.99 -35.68 Td[(=)-277(\050)]TJ/F44 10.91 Tf 15.75 0 Td[( )]TJ/F15 10.91 Tf 8.49 0 Td[(1\051)]TJ/F43 7.97 Tf 9.7 4.51 Td[(n)]TJ/F41 7.97 Tf 5.13 0 Td[(+1)]TJ/F42 10.91 Tf 50.66 2.87 Td[(q)]TJ/F26 5.98 Tf 6.46 8.33 Td[(n)]TJ/F24 5.98 Tf 4.6 0 Td[(\050)]TJ/F26 5.98 Tf 2.88 0 Td[(n)]TJ/F24 5.98 Tf 4.6 0 Td[(+1)]TJ ET -96.88 -22.18 21.32 0.36 re f 1 0 0 1 -88.05 -27.12 cm BT /F24 5.98 Tf 0 0 Td[(2)]TJ/F42 10.91 Tf 14.19 -1.18 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(n)]TJ/F41 7.97 Tf 5.13 0 Td[(+1)]TJ ET -53.43 -6.05 126.16 0.44 re f 1 0 0 1 -53.43 -16.04 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.36 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)-36(t)]TJ/F15 10.91 Tf 9.2 0 Td[(\051)]TJ/F44 10.91 Tf 6.06 0 Td[()-167()-166()]TJ/F15 10.91 Tf 14.55 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(n)]TJ/F42 10.91 Tf 5.63 -3.15 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ 8.47 7.48 Td[(=)-278(\050)]TJ/F44 10.91 Tf 15.76 0 Td[( )]TJ/F15 10.91 Tf 8.48 0 Td[(1\051)]TJ/F43 7.97 Tf 9.7 4.51 Td[(n)]TJ/F41 7.97 Tf 5.14 0 Td[(+1)]TJ/F42 10.91 Tf 11.32 -4.51 Td[(q)]TJ/F26 5.98 Tf 6.46 7.77 Td[(nE)]TJ ET 187.24 13.8 10.3 0.36 re f 1 0 0 1 190.56 8.86 cm BT /F24 5.98 Tf 0 0 Td[(2)]TJ/F42 10.91 Tf 8.67 -1.38 Td[(t)]TJ/F43 7.97 Tf 3.94 4.51 Td[(E)]TJ/F42 10.91 Tf 7.15 -4.51 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.66 4.51 Td[(n)]TJ/F42 10.91 Tf 5.64 -4.51 Td[(;)-166(t)]TJ/F15 10.91 Tf 8.79 0 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(;)]TJ/F15 10.91 Tf -364.34 -23.46 Td[(so)-334(that)-332(w)27(e)-333(ha)28(v)28(e)-334(\0501.2\051.)]TJ 11.95 -12.95 Td[(No)27(w,)-273(ob)29(viously)84(,)-273(from)]TJ/F42 10.91 Tf 101.9 0 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F42 10.91 Tf 5.64 -3.96 Td[(;)-166(t)]TJ/F15 10.91 Tf 8.79 0 Td[(\051,)-272(w)27(e)-258(see)-260(that)]TJ/F42 10.91 Tf 65.12 0 Td[(B)]TJ/F43 7.97 Tf 8.28 -1.64 Td[(i)]TJ/F15 10.91 Tf 6.41 1.64 Td[(=)-278(0)-258(if)]TJ/F42 10.91 Tf 28.97 0 Td[(i)]TJ/F15 10.91 Tf 6.57 0 Td[(is)-259(o)-27(dd)-258(and)]TJ/F42 10.91 Tf 51.24 0 Td[(B)]TJ/F43 7.97 Tf 8.28 -1.64 Td[(i)]TJ/F15 10.91 Tf 6.41 1.64 Td[(=)-277(1)-259(if)]TJ/F42 10.91 Tf 28.97 0 Td[(i)]TJ/F15 10.91 Tf 6.57 0 Td[(is)-259(ev)28(en.)-419(Hence)]TJ/F42 10.91 Tf -364.24 -19.54 Td[(E)]TJ/F15 10.91 Tf 11.83 0 Td[(=)]TJ/F42 10.91 Tf 11.62 0 Td[(n)]TJ/F15 10.91 Tf 9.02 0 Td[(+)-226(1)-288(=)]TJ/F46 10.91 Tf 31.18 8.18 Td[(P)]TJ/F41 7.97 Tf 11.52 -3.15 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(n)]TJ -4.23 -8.26 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=0)]TJ/F15 10.91 Tf 11.32 3.23 Td[(\050)]TJ/F44 10.91 Tf 4.24 0 Td[( )]TJ/F15 10.91 Tf 8.49 0 Td[(1\051)]TJ/F43 7.97 Tf 9.69 3.96 Td[(i)]TJ/F42 10.91 Tf 3.39 -3.96 Td[(B)]TJ/F43 7.97 Tf 8.27 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.38 1.64 Td[(,)-341(indeed.)-462(Also,)-341(for)]TJ/F50 10.91 Tf 90.23 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F51 7.97 Tf 0 -7.24 Td[(C)]TJ/F15 10.91 Tf 6.25 3.28 Td[(,)-341(w)27(e)-339(had)]TJ/F42 10.91 Tf 44.16 0 Td[(H)]TJ/F43 7.97 Tf 9.96 3.96 Td[(i)]TJ/F15 10.91 Tf 3.38 -3.96 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F51 7.97 Tf 0 -7.24 Td[(C)]TJ/F42 10.91 Tf 6.25 3.28 Td[(;)]TJ/F50 10.91 Tf 4.85 0 Td[(Z)]TJ/F15 10.91 Tf 7.27 0 Td[(\051)-288(=)]TJ/F46 10.91 Tf 19.02 15.38 Td[()]TJ/F50 10.91 Tf 13.16 -8.77 Td[(Z)]TJ/F42 10.91 Tf 17.24 0 Td[(i)]TJ/F15 10.91 Tf 6.79 0 Td[(:)-610(ev)27(en)]TJ -24.03 -12.95 Td[(0)]TJ/F42 10.91 Tf 17.24 0 Td[(i)]TJ/F15 10.91 Tf 6.79 0 Td[(:)-610(o)-28(dd)]TJ/F42 10.91 Tf 42.54 6.34 Td[(;)]TJ/F15 10.91 Tf 6.73 0 Td[(so)]TJ -422.24 -20.59 Td[(that)]TJ/F42 10.91 Tf 22.68 0 Td[(B)]TJ/F43 7.97 Tf 8.28 -1.63 Td[(i)]TJ/F15 10.91 Tf 6.06 1.63 Td[(indeed)-245(is)-246(rk)]TJ/F42 10.91 Tf 53.63 0 Td[(H)]TJ/F43 7.97 Tf 9.96 3.96 Td[(i)]TJ/F15 10.91 Tf 3.38 -3.96 Td[(\050)]TJ/F50 10.91 Tf 4.24 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F51 7.97 Tf 0 -7.24 Td[(C)]TJ/F42 10.91 Tf 6.25 3.28 Td[(;)]TJ/F50 10.91 Tf 4.85 0 Td[(Z)]TJ/F15 10.91 Tf 7.27 0 Td[(\051.)-415(This)-246(one)-246(sho)28(ws)-246(\0501.4\051.)-414(Hence)]TJ/F50 10.91 Tf 146.64 0 Td[(P)]TJ/F43 7.97 Tf 6.67 3.96 Td[(n)]TJ/F15 10.91 Tf 8.31 -3.96 Td[(satis\014es)-247(the)-245(W)83(eil)-245(conjectures.)]TJ/F41 7.97 Tf -81.01 -11.95 Td[(1)]TJ ET endstream endobj 4 0 obj 23476 endobj 1 0 obj << /Font << /F39 5 0 R /F15 6 0 R /F40 7 0 R /F38 8 0 R /F42 9 0 R /F46 10 0 R /F43 11 0 R /F45 12 0 R /F41 13 0 R /F50 14 0 R /F26 15 0 R /F52 16 0 R /F44 17 0 R /F24 18 0 R /F28 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7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F15 10.91 Tf 14.27 20.34 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(q)]TJ/F45 7.97 Tf 5.26 3.95 Td[( )]TJ/F43 7.97 Tf 6.59 0 Td[(s)]TJ/F15 10.91 Tf 4.41 -3.95 Td[(\051)]TJ/F43 7.97 Tf 4.24 3.95 Td[(r)]TJ/F41 7.97 Tf 5.47 0 Td[(deg)]TJ/F43 7.97 Tf 14.23 0 Td[(x)]TJ ET -341.44 -29.03 49.71 0.44 re f 1 0 0 1 -319.19 -39.02 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 28.66 7.49 Td[(\051)-278(=)-277(exp\050)]TJ/F46 10.91 Tf 40.82 10.36 Td[(X)]TJ/F43 7.97 Tf -1.12 -23.63 Td[(x)]TJ/F45 7.97 Tf 4.77 0 Td[(2)]TJ/F43 7.97 Tf 5.64 0 Td[(X)]TJ/F45 7.97 Tf 13.05 26.9 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.27 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.05 0 Td[(=1)]TJ/F15 10.91 Tf 14.28 20.34 Td[(\050deg)]TJ/F42 10.91 Tf 22.57 0 Td[(x)]TJ/F15 10.91 Tf 6.24 0 Td[(\051\050)]TJ/F42 10.91 Tf 8.48 0 Td[(q)]TJ/F45 7.97 Tf 5.26 3.95 Td[( )]TJ/F43 7.97 Tf 6.59 0 Td[(s)]TJ/F15 10.91 Tf 4.41 -3.95 Td[(\051)]TJ/F43 7.97 Tf 4.25 3.95 Td[(r)]TJ/F41 7.97 Tf 5.46 0 Td[(deg)]TJ/F43 7.97 Tf 14.24 0 Td[(x)]TJ ET 106.95 9.99 82.76 0.44 re f 1 0 0 1 132.52 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 7.05 0 Td[(deg)]TJ/F42 10.91 Tf 18.33 0 Td[(x)]TJ/F15 10.91 Tf 33.01 7.49 Td[(\051)-277(=)-278(exp\050)]TJ/F46 10.91 Tf 40.81 10.36 Td[(X)]TJ/F43 7.97 Tf -1.12 -23.63 Td[(x)]TJ/F45 7.97 Tf 4.77 0 Td[(2)]TJ/F43 7.97 Tf 5.65 0 Td[(X)]TJ/F45 7.97 Tf 13.15 26.9 Td[(1)]TJ/F46 10.91 Tf -3.65 -3.27 Td[(X)]TJ/F43 7.97 Tf -0.1 -23.32 Td[(n)]TJ/F41 7.97 Tf 5.14 0 Td[(=1)]TJ/F42 10.91 Tf 13.83 20.34 Td[(N)]TJ/F43 7.97 Tf 8.77 -1.64 Td[(n)]TJ/F15 10.91 Tf 5.63 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(x)]TJ/F15 10.91 Tf 6.23 0 Td[(\051\050)]TJ/F42 10.91 Tf 8.49 0 Td[(q)]TJ/F45 7.97 Tf 5.26 3.95 Td[( )]TJ/F43 7.97 Tf 6.58 0 Td[(s)]TJ/F15 10.91 Tf 4.42 -3.95 Td[(\051)]TJ/F43 7.97 Tf 4.24 3.95 Td[(n)]TJ ET 136.87 9.99 59.5 0.44 re f 1 0 0 1 163.35 0 cm BT /F42 10.91 Tf 0 0 Td[(n)]TJ/F15 10.91 Tf 34.22 7.49 Td[(\051)]TJ -290.58 -36.75 Td[(=)-277(exp\050)]TJ/F45 7.97 Tf 36.17 13.63 Td[(1)]TJ/F46 10.91 Tf -3.65 -3.27 Td[(X)]TJ/F43 7.97 Tf -0.1 -23.32 Td[(n)]TJ/F41 7.97 Tf 5.14 0 Td[(=1)]TJ/F42 10.91 Tf 12.64 12.96 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(n)]TJ/F15 10.91 Tf 6.84 9.02 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(q)]TJ/F45 7.97 Tf 5.26 3.96 Td[( )]TJ/F43 7.97 Tf 6.59 0 Td[(s)]TJ/F15 10.91 Tf 4.41 -3.96 Td[(\051)]TJ/F43 7.97 Tf 4.24 3.96 Td[(n)]TJ ET -190.56 -26.75 30.38 0.44 re f 1 0 0 1 -178.65 -36.75 cm BT /F42 10.91 Tf 0 0 Td[(n)]TJ/F15 10.91 Tf 22.69 7.49 Td[(=)]TJ/F42 10.91 Tf 11.52 0 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)-23(;)-167(q)]TJ/F45 7.97 Tf 19.4 4.5 Td[( )]TJ/F43 7.97 Tf 6.58 0 Td[(s)]TJ/F15 10.91 Tf 4.42 -4.5 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F38 10.91 Tf -294 -31.09 Td[(Exercise)-450(5.5.)]TJ/F15 10.91 Tf 75.42 0 Td[(By)-392(the)-391(W)84(eil)-392(conjectures,)-406(since)-392(dim)]TJ/F42 10.91 Tf 170.61 0 Td[(H)]TJ/F41 7.97 Tf 9.95 3.96 Td[(1)]TJ/F15 10.91 Tf 4.73 -3.96 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(X)-23(;)]TJ/F50 10.91 Tf 14.13 0 Td[(Q)]TJ/F43 7.97 Tf 8.49 -1.77 Td[(l)]TJ/F15 10.91 Tf 3.12 1.77 Td[(\051)-374(=)]TJ/F42 10.91 Tf 20.9 0 Td[(B)]TJ/F41 7.97 Tf 8.28 -1.63 Td[(1)]TJ/F15 10.91 Tf 8.82 1.63 Td[(=)-374(deg)]TJ/F42 10.91 Tf 30.91 0 Td[(P)]TJ/F41 7.97 Tf 7 -1.63 Td[(1)]TJ/F15 10.91 Tf 4.73 1.63 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)-375(=)-374(2)]TJ/F42 10.91 Tf 26.36 0 Td[(g)]TJ/F15 10.91 Tf 5.6 0 Td[(,)-406(for)]TJ -411.48 -12.95 Td[(some)]TJ/F42 10.91 Tf 27.33 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.63 Td[(i)]TJ/F15 10.91 Tf 3.38 1.63 Td[(,)-333(w)27(e)-333(ha)28(v)28(e)]TJ/F42 10.91 Tf 76.29 -21.3 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)-24(;)-166(t)]TJ/F15 10.91 Tf 18.08 0 Td[(\051)-277(=)]TJ/F42 10.91 Tf 41.74 7.38 Td[(P)]TJ/F41 7.97 Tf 7.01 -1.64 Td[(1)]TJ/F15 10.91 Tf 4.73 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ ET -48.17 -55.34 67.69 0.44 re f 1 0 0 1 -48.17 -65.34 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F42 10.91 Tf 10.9 0 Td[(q)-37(t)]TJ/F15 10.91 Tf 9.2 0 Td[(\051)]TJ 8.47 7.49 Td[(=)]TJ/F46 10.91 Tf 13.52 15.69 Td[(Q)]TJ/F41 7.97 Tf 10.3 -2.88 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(g)]TJ -4.24 -8.56 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F15 10.91 Tf 11.32 3.26 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F42 10.91 Tf 3.38 1.64 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ ET 84.62 10 67.69 0.44 re f 1 0 0 1 84.62 0 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)-36(t)]TJ/F15 10.91 Tf 9.2 0 Td[(\051)]TJ -218.43 -26.9 Td[(=)-277(exp\050)]TJ/F45 7.97 Tf 36.07 13.64 Td[(1)]TJ/F46 10.91 Tf -3.65 -3.28 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.31 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F15 10.91 Tf 11.26 12.95 Td[(\050)]TJ/F42 10.91 Tf 5.44 7.38 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET -101.36 -24.39 8.49 0.44 re f 1 0 0 1 -99.73 -34.38 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 10.48 7.48 Td[(+)]TJ/F42 10.91 Tf 12.1 7.38 Td[(q)]TJ/F43 7.97 Tf 5.27 3.96 Td[(r)]TJ/F42 10.91 Tf 4.55 -3.96 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET 22.58 9.99 18.31 0.44 re f 1 0 0 1 29.13 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F44 10.91 Tf 15.38 7.48 Td[( )]TJ/F41 7.97 Tf 14.52 14.22 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ/F46 10.91 Tf -7.84 -3.86 Td[(X)]TJ/F43 7.97 Tf 1.03 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F42 10.91 Tf 13.67 13.09 Td[()]TJ/F43 7.97 Tf 7.02 4.5 Td[(r)]TJ -0.04 -7.2 Td[(i)]TJ/F42 10.91 Tf 5.79 10.08 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET 56.64 9.99 8.49 0.44 re f 1 0 0 1 58.27 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.06 7.48 Td[(\051\051)-277(=)-278(exp\050)]TJ/F45 7.97 Tf 47.58 13.64 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.28 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.31 Td[(r)]TJ/F41 7.97 Tf 4.05 0 Td[(=1)]TJ/F42 10.91 Tf 13.08 12.95 Td[(N)]TJ/F43 7.97 Tf 8.77 -1.64 Td[(r)]TJ/F42 10.91 Tf 5.75 9.02 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET 84.09 9.99 8.49 0.44 re f 1 0 0 1 85.72 0 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 8.06 7.48 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F15 10.91 Tf -322.87 -28.12 Td[(Hence,)]TJ/F42 10.91 Tf 35.46 0 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.64 Td[(r)]TJ/F15 10.91 Tf 7.59 1.64 Td[(=)-277(1)-223(+)]TJ/F42 10.91 Tf 30.3 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(r)]TJ/F44 10.91 Tf 6.98 -3.96 Td[( )]TJ/F46 10.91 Tf 10.91 8.18 Td[(P)]TJ/F41 7.97 Tf 11.52 -2.87 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ -4.23 -8.57 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F42 10.91 Tf 13.14 3.26 Td[()]TJ/F43 7.97 Tf 7.02 3.96 Td[(r)]TJ -0.04 -7.01 Td[(i)]TJ/F15 10.91 Tf 8.23 3.05 Td[(for)-332(all)]TJ/F42 10.91 Tf 31.84 0 Td[(r)]TJ/F44 10.91 Tf 8.26 0 Td[()]TJ/F15 10.91 Tf 11.52 0 Td[(1.)]TJ -199.63 -12.95 Td[(No)27(w,)-333(from)-332(the)-334(functional)-331(equation,)-331(w)27(e)-333(ha)28(v)28(e)]TJ/F42 10.91 Tf 144.19 -28.59 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ 7.31 7.38 Td[(1)]TJ ET -152.72 -59.67 9.2 0.44 re f 1 0 0 1 -152.72 -69.67 cm BT /F42 10.91 Tf 0 0 Td[(q)-37(t)]TJ/F15 10.91 Tf 10.4 7.49 Td[(\051)-278(=)]TJ/F44 10.91 Tf 18.79 0 Td[()]TJ/F42 10.91 Tf 8.48 0 Td[(q)]TJ/F41 7.97 Tf 5.26 4.5 Td[(1)]TJ/F45 7.97 Tf 4.24 0 Td[( )]TJ/F43 7.97 Tf 6.58 0 Td[(g)]TJ/F42 10.91 Tf 4.82 -4.5 Td[(t)]TJ/F41 7.97 Tf 3.94 4.5 Td[(2)]TJ/F45 7.97 Tf 4.23 0 Td[( )]TJ/F41 7.97 Tf 6.59 0 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ/F42 10.91 Tf 4.82 -4.5 Td[(Z)]TJ/F15 10.91 Tf 8.22 0 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F15 10.91 Tf -260.88 -20.68 Td[(The)-334(left)-333(hand)-331(side)-334(of)-333(the)-333(equation)-332(is,)]TJ/F46 10.91 Tf 100.36 -11.24 Td[(Q)]TJ/F41 7.97 Tf 10.3 -2.87 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ -4.23 -8.57 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F15 10.91 Tf 11.32 3.26 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F43 7.97 Tf 12.11 4.6 Td[()]TJ/F26 5.98 Tf 5.43 -1.22 Td[(i)]TJ ET -8.76 -30.1 8.6 0.44 re f 1 0 0 1 -8.03 -36.37 cm BT /F43 7.97 Tf 0 0 Td[(q)-37(t)]TJ/F15 10.91 Tf 9.06 3.76 Td[(\051)]TJ ET -53.42 -3.3 70.69 0.44 re f 1 0 0 1 -53.42 -14.04 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F41 7.97 Tf 13.55 4.3 Td[(1)]TJ ET 24.22 2.51 7.12 0.44 re f 1 0 0 1 24.22 -3.76 cm BT /F43 7.97 Tf 0 0 Td[(q)-37(t)]TJ/F15 10.91 Tf 8.32 3.76 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F41 7.97 Tf 12.1 4.3 Td[(1)]TJ ET 36.79 6.27 4.23 0.44 re f 1 0 0 1 37.38 0 cm BT /F43 7.97 Tf 0 0 Td[(t)]TJ/F15 10.91 Tf 4.84 3.76 Td[(\051)]TJ 8.47 8.23 Td[(=)]TJ/F42 10.91 Tf 12.71 10.66 Td[(t)]TJ/F41 7.97 Tf 3.94 3.96 Td[(2)]TJ/F45 7.97 Tf 4.23 0 Td[( )]TJ/F41 7.97 Tf 6.59 0 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ/F42 10.91 Tf 4.82 -3.96 Td[(q)]TJ/F41 7.97 Tf 5.26 3.96 Td[(1)]TJ/F45 7.97 Tf 4.23 0 Td[( )]TJ/F43 7.97 Tf 6.59 0 Td[(g)]TJ/F46 10.91 Tf 6.63 4.22 Td[(Q)]TJ/F41 7.97 Tf 10.3 -2.87 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(g)]TJ -4.24 -8.57 Td[(i)]TJ/F41 7.97 Tf 2.89 0 Td[(=1)]TJ/F15 10.91 Tf 11.32 3.26 Td[(\050)]TJ/F44 10.91 Tf 4.24 6.8 Td[(p)]TJ ET 110.38 29.45 5.26 0.44 re f 1 0 0 1 110.38 22.65 cm BT /F42 10.91 Tf 0 0 Td[(q)-36(t)]TJ/F44 10.91 Tf 11.62 0 Td[( )]TJ/F43 7.97 Tf 13.37 4.6 Td[()]TJ/F26 5.98 Tf 5.44 -1.22 Td[(i)]TJ ET 23.73 2.51 11.12 0.44 re f 1 0 0 1 23.73 1.21 cm BT /F45 7.97 Tf 0 0 Td[(p)]TJ ET 7.06 0 4.07 0.36 re f 1 0 0 1 7.06 -4.97 cm BT /F43 7.97 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 5.26 3.76 Td[(\051)]TJ ET -115.15 -4.39 124.65 0.44 re f 1 0 0 1 -86.67 -14.38 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F42 10.91 Tf 10.9 0 Td[(q)-37(t)]TJ/F15 10.91 Tf 9.21 0 Td[(\051)]TJ/F42 10.91 Tf 33.92 7.48 Td[(:)]TJ/F15 10.91 Tf -309.87 -26.88 Td[(Hence,)-334(b)28(y)-333(comparing)-332(terms,)-334(w)28(e)-334(ha)28(v)28(e)]TJ/F42 10.91 Tf 107.6 -28.33 Td[(P)]TJ/F41 7.97 Tf 7.01 -1.63 Td[(1)]TJ/F15 10.91 Tf 4.73 1.63 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)-278(=)]TJ/F41 7.97 Tf 21.49 14.22 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ/F46 10.91 Tf -6.93 -3.85 Td[(Y)]TJ/F43 7.97 Tf 0.12 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F15 10.91 Tf 10.94 13.08 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.63 Td[(i)]TJ/F42 10.91 Tf 3.38 1.63 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)-278(=)]TJ/F44 10.91 Tf 18.79 0 Td[()]TJ/F41 7.97 Tf 12.99 14.22 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(g)]TJ/F46 10.91 Tf -6.93 -3.85 Td[(Y)]TJ/F43 7.97 Tf 0.12 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F15 10.91 Tf 10.94 13.08 Td[(\050)]TJ/F44 10.91 Tf 4.24 7.33 Td[(p)]TJ ET 41.44 -40.4 5.26 0.44 re f 1 0 0 1 41.44 -47.73 cm BT /F42 10.91 Tf 0 0 Td[(q)-36(t)]TJ/F44 10.91 Tf 11.63 0 Td[( )]TJ/F42 10.91 Tf 14.1 7.38 Td[()]TJ/F43 7.97 Tf 6.98 -1.63 Td[(i)]TJ ET 23.73 2.51 14.35 0.44 re f 1 0 0 1 23.73 -0.68 cm BT /F44 10.91 Tf 0 0 Td[(p)]TJ ET 9.09 0 5.26 0.44 re f 1 0 0 1 9.09 -6.8 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 6.46 7.48 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F15 10.91 Tf -297.46 -29.77 Td[(Recall)-290(that)]TJ/F41 7.97 Tf 66.82 4.3 Td[(1)]TJ ET -230 -19.78 24.35 0.44 re f 1 0 0 1 -230 -26.05 cm BT /F45 7.97 Tf 0 0 Td[( )]TJ/F43 7.97 Tf 6.58 0 Td[(a)]TJ/F41 7.97 Tf 4.5 0 Td[(+)]TJ/F43 7.97 Tf 6.59 0 Td[(bt)]TJ/F15 10.91 Tf 10.91 3.76 Td[(=)]TJ/F45 7.97 Tf 12.71 4.3 Td[( )]TJ/F41 7.97 Tf 6.58 0 Td[(1)]TJ ET 41.29 6.27 10.82 0.44 re f 1 0 0 1 44.45 0 cm BT /F43 7.97 Tf 0 0 Td[(a)]TJ/F15 10.91 Tf 8.85 3.76 Td[(\0501)-135(+)]TJ/F43 7.97 Tf 22.75 4.3 Td[(b)]TJ ET 31.16 6.27 4.5 0.44 re f 1 0 0 1 31.16 0 cm BT /F43 7.97 Tf 0 0 Td[(a)]TJ/F42 10.91 Tf 5.7 3.76 Td[(t)]TJ/F15 10.91 Tf 5.4 0 Td[(+)-135(\050)]TJ/F43 7.97 Tf 15.83 4.3 Td[(b)]TJ ET 26.5 6.27 4.5 0.44 re f 1 0 0 1 26.5 0 cm BT /F43 7.97 Tf 0 0 Td[(a)]TJ/F15 10.91 Tf 5.69 3.76 Td[(\051)]TJ/F41 7.97 Tf 4.24 3.96 Td[(2)]TJ/F42 10.91 Tf 4.73 -3.96 Td[(t)]TJ/F41 7.97 Tf 3.94 3.96 Td[(2)]TJ/F15 10.91 Tf 6.2 -3.96 Td[(+)]TJ/F44 10.91 Tf 9.95 0 Td[()-167()-166()]TJ/F15 10.91 Tf 14.55 0 Td[(\051)-289(so)-290(that)-289(log)-13(\050)]TJ/F44 10.91 Tf 61.81 0 Td[( )]TJ/F42 10.91 Tf 8.48 0 Td[(a)]TJ/F15 10.91 Tf 7.24 0 Td[(+)]TJ/F42 10.91 Tf 9.95 0 Td[(bt)]TJ/F15 10.91 Tf 8.62 0 Td[(\051)-278(=)]TJ/F44 10.91 Tf 18.79 0 Td[( )]TJ/F15 10.91 Tf 8.48 0 Td[(\050)]TJ/F43 7.97 Tf 5.88 4.3 Td[(b)]TJ ET 178.11 6.27 4.5 0.44 re f 1 0 0 1 178.11 0 cm BT /F43 7.97 Tf 0 0 Td[(a)]TJ/F42 10.91 Tf 5.69 3.76 Td[(t)]TJ/F15 10.91 Tf 5.41 0 Td[(+)-134(\050)]TJ/F43 7.97 Tf 15.83 4.3 Td[(b)]TJ ET 26.49 6.27 4.5 0.44 re f 1 0 0 1 26.49 0 cm BT /F43 7.97 Tf 0 0 Td[(a)]TJ/F15 10.91 Tf 5.69 3.76 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11.62 0 Td[( )]TJ/F15 10.91 Tf 18.38 10.26 Td[()]TJ/F42 10.91 Tf -2.35 -2.88 Td[(f)]TJ ET 23.73 2.51 14.35 0.44 re f 1 0 0 1 23.73 -0.68 cm BT /F44 10.91 Tf 0 0 Td[(p)]TJ ET 9.09 0 5.26 0.44 re f 1 0 0 1 9.09 -6.8 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 6.46 7.48 Td[(\051)]TJ -342.36 -29.19 Td[(so)-334(that)]TJ/F44 10.91 Tf 129.51 -17.87 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[(a)]TJ/F44 10.91 Tf 5.76 0 Td[(j)]TJ/F15 10.91 Tf 6.06 0 Td[(=)]TJ/F44 10.91 Tf 11.52 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[(f)]TJ/F15 10.91 Tf 8.94 0 Td[(+)]TJ 13.26 2.88 Td[()]TJ/F42 10.91 Tf -2.35 -2.88 Td[(f)]TJ/F44 10.91 Tf 6.51 0 Td[(j)-278()]TJ/F15 10.91 Tf 17.58 0 Td[(2)]TJ/F42 10.91 Tf 5.45 0 Td[(g)]TJ/F44 10.91 Tf 8.63 0 Td[(,)-277(j)]TJ/F42 10.91 Tf 16.97 0 Td[(f)]TJ/F44 10.91 Tf 6.51 0 Td[(j)]TJ/F15 10.91 Tf 6.06 0 Td[(=)]TJ/F44 10.91 Tf 11.52 0 Td[(j)]TJ/F15 10.91 Tf 5.38 2.88 Td[()]TJ/F42 10.91 Tf -2.35 -2.88 Td[(f)]TJ/F44 10.91 Tf 6.51 0 Td[(j)]TJ/F15 10.91 Tf 6.06 0 Td[(=)]TJ/F44 10.91 Tf 11.52 7.33 Td[(p)]TJ ET -41.7 -32.25 5.26 0.44 re f 1 0 0 1 -41.7 -39.58 cm BT /F42 10.91 Tf 0 0 Td[(q)-36(:)]TJ/F15 10.91 Tf -282.25 -20.14 Td[(\050See)-334(Exercise)-334(5.7,)-333(\050b\051)-333(and)-332(\050c\051.\051)]TJ/F38 10.91 Tf -11.95 -29.28 Td[(Exercise)-383(5.7.)]TJ/F52 10.91 Tf 0 -29.27 Td[(\050a\051.)]TJ/F15 10.91 Tf 23.3 0 Td[(W)84(e)-334(ha)29(v)28(e)]TJ/F42 10.91 Tf 90.68 -26.6 Td[(Z)]TJ/F15 10.91 Tf 8.23 0 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(X)-24(;)-166(t)]TJ/F15 10.91 Tf 18.08 0 Td[(\051)-277(=)]TJ/F42 10.91 Tf 41.74 7.38 Td[(P)]TJ/F41 7.97 Tf 7.01 -1.64 Td[(1)]TJ/F15 10.91 Tf 4.73 1.64 Td[(\050)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ ET -129.69 -102.78 67.69 0.44 re f 1 0 0 1 -129.69 -112.77 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F42 10.91 Tf 10.9 0 Td[(q)-37(t)]TJ/F15 10.91 Tf 9.2 0 Td[(\051)]TJ 8.47 7.48 Td[(=)]TJ/F46 10.91 Tf 13.52 15.69 Td[(Q)]TJ/F41 7.97 Tf 10.3 -2.87 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(g)]TJ -4.24 -8.57 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F15 10.91 Tf 11.32 3.26 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F42 10.91 Tf 3.38 1.64 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051)]TJ ET 84.62 9.99 67.69 0.44 re f 1 0 0 1 84.62 0 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(t)]TJ/F15 10.91 Tf 3.94 0 Td[(\051\0501)]TJ/F44 10.91 Tf 16.37 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(q)-36(t)]TJ/F15 10.91 Tf 9.2 0 Td[(\051)]TJ -175.43 -34 Td[(=)-278(exp\050)]TJ/F45 7.97 Tf 36.07 13.64 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.28 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.06 0 Td[(=1)]TJ/F15 10.91 Tf 14.27 20.47 Td[(\0501)]TJ/F44 10.91 Tf 12.12 0 Td[( )]TJ/F46 10.91 Tf 10.91 8.18 Td[(P)]TJ/F41 7.97 Tf 11.52 -2.87 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ -4.23 -8.57 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F42 10.91 Tf 13.14 3.26 Td[()]TJ/F43 7.97 Tf 7.01 3.96 Td[(r)]TJ -0.04 -7.01 Td[(i)]TJ/F15 10.91 Tf 7.02 3.05 Td[(+)]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(r)]TJ/F15 10.91 Tf 4.56 -3.96 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(t)]TJ/F43 7.97 Tf 3.94 3.96 Td[(r)]TJ ET -60.78 -31.49 98.02 0.44 re f 1 0 0 1 -14.38 -41.48 cm BT /F42 10.91 Tf 0 0 Td[(r)]TJ/F15 10.91 Tf 52.82 7.48 Td[(\051)]TJ/F42 10.91 Tf 4.24 0 Td[(:)]TJ/F15 10.91 Tf -279.86 -32.68 Td[(Hence,)]TJ/F42 10.91 Tf 35.46 0 Td[(N)]TJ/F43 7.97 Tf 8.76 -1.63 Td[(r)]TJ/F15 10.91 Tf 7.59 1.63 Td[(=)-277(1)]TJ/F44 10.91 Tf 19.39 0 Td[( )]TJ/F46 10.91 Tf 10.91 8.19 Td[(P)]TJ/F41 7.97 Tf 11.52 -2.88 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ -4.23 -8.56 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F42 10.91 Tf 13.14 3.25 Td[()]TJ/F43 7.97 Tf 7.02 3.96 Td[(r)]TJ -0.04 -7.01 Td[(i)]TJ/F15 10.91 Tf 7.02 3.05 Td[(+)]TJ/F42 10.91 Tf 10.9 0 Td[(q)]TJ/F43 7.97 Tf 5.27 3.96 Td[(r)]TJ/F15 10.91 Tf 7.58 -3.96 Td[(=)-278(1)]TJ/F44 10.91 Tf 19.39 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[(a)]TJ/F43 7.97 Tf 5.77 -1.63 Td[(r)]TJ/F15 10.91 Tf 6.98 1.63 Td[(+)]TJ/F42 10.91 Tf 10.91 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.96 Td[(r)]TJ/F15 10.91 Tf 8.19 -3.96 Td[(so)-334(that)]TJ/F42 10.91 Tf 37.03 0 Td[(a)]TJ/F43 7.97 Tf 5.77 -1.63 Td[(r)]TJ/F15 10.91 Tf 7.58 1.63 Td[(=)]TJ/F46 10.91 Tf 11.52 8.19 Td[(P)]TJ/F41 7.97 Tf 11.51 -2.88 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(g)]TJ -4.24 -8.56 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F15 10.91 Tf 11.32 3.25 Td[(\050)]TJ/F42 10.91 Tf 4.25 0 Td[()]TJ/F43 7.97 Tf 6.97 -1.63 Td[(i)]TJ/F15 10.91 Tf 3.39 1.63 Td[(\051)]TJ/F43 7.97 Tf 4.24 3.96 Td[(r)]TJ/F15 10.91 Tf 4.55 -3.96 Td[(.)]TJ/F52 10.91 Tf -337.77 -29.27 Td[(\050b\051.)]TJ/F15 10.91 Tf 22.74 0 Td[(\050)]TJ/F44 10.91 Tf 4.24 0 Td[(\050)]TJ/F15 10.91 Tf 10.91 0 Td[(\051)-333(If)]TJ/F44 10.91 Tf 18.79 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F44 10.91 Tf 3.38 1.64 Td[(j)-277()]TJ 17.57 6.8 Td[(p)]TJ ET -138.02 -47.67 5.26 0.44 re f 1 0 0 1 -138.02 -54.47 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 8.9 0 Td[(for)-333(all)]TJ/F42 10.91 Tf 31.85 0 Td[(i)]TJ/F15 10.91 Tf 3.76 0 Td[(,)-333(then,)]TJ/F44 10.91 Tf -9.28 -34.57 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F44 10.91 Tf 3.38 1.64 Td[(j)-278()]TJ/F41 7.97 Tf 21.18 14.21 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ/F46 10.91 Tf -7.83 -3.85 Td[(X)]TJ/F43 7.97 Tf 1.02 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.89 0 Td[(=1)]TJ/F44 10.91 Tf 13.66 13.09 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F44 10.91 Tf 3.38 1.64 Td[(j)]TJ/F43 7.97 Tf 3.03 4.5 Td[(r)]TJ/F44 10.91 Tf 7.59 -4.5 Td[()]TJ/F41 7.97 Tf 15.12 14.21 Td[(2)]TJ/F43 7.97 Tf 4.23 0 Td[(g)]TJ/F46 10.91 Tf -7.84 -3.85 Td[(X)]TJ/F43 7.97 Tf 1.03 -23.45 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F44 10.91 Tf 13.67 21.36 Td[(p)]TJ ET 145.96 -26.3 9.82 0.44 re f 1 0 0 1 145.96 -34.57 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(r)]TJ/F15 10.91 Tf 7.59 -3.15 Td[(=)-277(2)]TJ/F42 10.91 Tf 16.97 0 Td[(g)]TJ/F44 10.91 Tf 5.59 8.27 Td[(p)]TJ ET 44.5 8.27 9.82 0.44 re f 1 0 0 1 44.5 0 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(r)]TJ/F42 10.91 Tf 4.56 -3.15 Td[(:)]TJ/F15 10.91 Tf -297.01 -32.81 Td[(\050)]TJ/F44 10.91 Tf 4.24 0 Td[(\051)]TJ/F15 10.91 Tf 10.91 0 Td[(\051)-333(Consider)-333(the)-333(follo)29(wing)-333(easy)-334(p)-27(o)28(w)27(er)-333(series)-334(expansion:)]TJ/F41 7.97 Tf 150.94 -19.41 Td[(2)]TJ/F43 7.97 Tf 4.24 0 Td[(g)]TJ/F46 10.91 Tf -7.84 -3.85 Td[(X)]TJ/F43 7.97 Tf 1.03 -23.46 Td[(i)]TJ/F41 7.97 Tf 2.88 0 Td[(=1)]TJ/F42 10.91 Tf 24.25 20.47 Td[()]TJ/F43 7.97 Tf 6.98 -1.63 Td[(i)]TJ/F42 10.91 Tf 3.38 1.63 Td[(t)]TJ ET -105.93 -63.93 33.09 0.44 re f 1 0 0 1 -105.93 -73.92 cm BT /F15 10.91 Tf 0 0 Td[(1)]TJ/F44 10.91 Tf 7.88 0 Td[( )]TJ/F42 10.91 Tf 10.91 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F42 10.91 Tf 3.38 1.64 Td[(t)]TJ/F15 10.91 Tf 8.16 7.48 Td[(=)]TJ/F45 7.97 Tf 15.16 13.64 Td[(1)]TJ/F46 10.91 Tf -3.64 -3.27 Td[(X)]TJ/F43 7.97 Tf 0.44 -23.32 Td[(r)]TJ/F41 7.97 Tf 4.05 0 Td[(=1)]TJ/F42 10.91 Tf 13.08 12.95 Td[(a)]TJ/F43 7.97 Tf 5.77 -1.63 Td[(r)]TJ/F42 10.91 Tf 4.55 1.63 Td[(t)]TJ/F43 7.97 Tf 3.94 4.51 Td[(r)]TJ/F42 10.91 Tf 4.56 -4.51 Td[(:)]TJ/F15 10.91 Tf -254.53 -34.06 Td[(Since)]TJ/F44 10.91 Tf 28.83 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[(a)]TJ/F43 7.97 Tf 5.77 -1.64 Td[(r)]TJ/F44 10.91 Tf 4.55 1.64 Td[(j)-329()]TJ/F15 10.91 Tf 18.71 0 Td[(2)]TJ/F42 10.91 Tf 5.45 0 Td[(g)]TJ/F44 10.91 Tf 5.6 7.74 Td[(p)]TJ ET -88.28 -18.84 9.82 0.44 re f 1 0 0 1 -88.28 -26.58 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F43 7.97 Tf 5.26 3.15 Td[(r)]TJ/F15 10.91 Tf 4.55 -3.15 Td[(,)-372(the)-365(RHS)-364(is)-364(holomorphic)-363(in)]TJ/F44 10.91 Tf 139.64 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[(t)]TJ/F44 10.91 Tf 3.94 0 Td[(j)]TJ/F42 10.91 Tf 6.63 0 Td[(<)]TJ/F41 7.97 Tf 16.72 4.3 Td[(1)]TJ ET 176.32 2.51 11.12 0.44 re f 1 0 0 1 176.32 1.21 cm BT /F45 7.97 Tf 0 0 Td[(p)]TJ ET 7.06 0 4.07 0.36 re f 1 0 0 1 7.06 -4.97 cm BT /F43 7.97 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 5.26 3.76 Td[(.)-538(If)]TJ/F44 10.91 Tf 20.15 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[()]TJ/F43 7.97 Tf 6.98 -1.64 Td[(i)]TJ/F44 10.91 Tf 3.38 1.64 Td[(j)]TJ/F42 10.91 Tf 6.63 0 Td[(>)]TJ/F44 10.91 Tf 12.08 6.8 Td[(p)]TJ ET 66.6 10.56 5.26 0.44 re f 1 0 0 1 66.6 3.76 cm BT /F42 10.91 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 9.24 0 Td[(for)-363(some)]TJ/F42 10.91 Tf 44.71 0 Td[(i)]TJ/F15 10.91 Tf 3.75 0 Td[(,)-372(then,)]TJ -400.66 -16.83 Td[(the)-333(LHS)-333(has)-333(a)-333(p)-27(ole)-334(of)-333(order)-332(1)-333(in)]TJ/F44 10.91 Tf 158.15 0 Td[(j)]TJ/F42 10.91 Tf 3.03 0 Td[(t)]TJ/F44 10.91 Tf 3.94 0 Td[(j)]TJ/F42 10.91 Tf 6.06 0 Td[(<)]TJ/F41 7.97 Tf 16.16 4.29 Td[(1)]TJ ET -159.07 -14.32 11.12 0.44 re f 1 0 0 1 -159.07 -15.62 cm BT /F45 7.97 Tf 0 0 Td[(p)]TJ ET 7.06 0 4.07 0.36 re f 1 0 0 1 7.06 -4.97 cm BT /F43 7.97 Tf 0 0 Td[(q)]TJ/F15 10.91 Tf 8.9 3.76 Td[(at)]TJ/F42 10.91 Tf 13.33 0 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