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10.3 0 Td[(Z)]TJ/F16 7.97 Tf 7.27 -1.63 Td[(2)]TJ/F15 10.91 Tf 4.74 1.63 Td[([)]TJ/F18 10.91 Tf 3.03 0 Td[(x)]TJ/F15 10.91 Tf 6.23 0 Td[(])-333(dar.)-443(Geb)-28(en)-333(Sie)]TJ/F18 10.91 Tf 82.23 0 Td[(d)]TJ/F15 10.91 Tf 5.68 0 Td[(,)]TJ/F18 10.91 Tf 6.66 0 Td[(a)]TJ/F15 10.91 Tf 9.41 0 Td[(und)]TJ/F18 10.91 Tf 21.81 0 Td[(b)]TJ/F15 10.91 Tf 8.32 0 Td[(an.)]TJ ET 7.7 -39.73 460.3 0.4 re f 7.7 -55.51 0.4 15.78 re f 467.6 -55.51 0.4 15.78 re f 7.7 -55.91 460.3 0.4 re f 1 0 0 1 16.47 -52.52 cm BT /F18 10.91 Tf 0 0 Td[(d)]TJ/F15 10.91 Tf 8.71 0 Td[(=)]TJ/F18 10.91 Tf 140.48 0 Td[(a)]TJ/F15 10.91 Tf 8.8 0 Td[(=)]TJ/F18 10.91 Tf 140.48 0 Td[(b)]TJ/F15 10.91 Tf 7.71 0 Td[(=)]TJ ET -16.47 -13.55 468 0.5 re f 1 0 0 1 -16.47 -32.14 cm BT /F35 10.91 Tf 0 0 Td[(Aufgab)-32(e)-384(R4.)]TJ/F15 10.91 Tf 80.39 0 Td[(\0505)-334(Punkte\051)]TJ -80.39 -16.92 Td[(Es)-334(sei)]TJ/F18 10.91 Tf 31.18 0 Td[(')]TJ/F15 10.91 Tf 10.77 0 Td[(die)-333(eulersc)27(he)]TJ/F18 10.91 Tf 64.03 0 Td[(')]TJ/F15 10.91 Tf 7.14 0 Td[(-F)83(unktion.)-442(Berec)27(hnen)-332(Sie)]TJ/F18 10.91 Tf 124.88 0 Td[(')]TJ/F15 10.91 Tf 7.14 0 Td[(\050100\051.)-692(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)]TJ ET 435.12 -4.13 32.88 0.4 re f 435.12 -19.91 0.4 15.78 re f 467.6 -19.91 0.4 15.78 re f 435.12 -20.3 32.88 0.4 re f 1 0 0 1 0 -37.33 cm BT /F15 10.91 Tf 0 0 Td[(Bestimmen)-334(Sie)-333(die)-333(kleinste)-334(Zahl)]TJ/F18 10.91 Tf 156.64 0 Td[(n)]TJ/F21 10.91 Tf 9.57 0 Td[(2)]TJ/F30 10.91 Tf 10.31 0 Td[(N)]TJ/F16 7.97 Tf 7.88 -1.63 Td[(0)]TJ/F15 10.91 Tf 8.36 1.63 Td[(mit)]TJ/F18 10.91 Tf 20 0 Td[(n)]TJ/F21 10.91 Tf 9.58 0 Td[()]TJ/F15 10.91 Tf 11.52 0 Td[(13)]TJ/F16 7.97 Tf 10.91 3.96 Td[(162)]TJ/F15 10.91 Tf 16.23 -3.96 Td[(mo)-28(d)-277(100.)-577(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)]TJ ET 435.12 12.8 32.88 0.4 re f 435.12 -2.98 0.4 15.78 re f 467.6 -2.98 0.4 15.78 re f 435.12 -3.38 32.88 0.4 re f 0 -13.55 468 0.5 re f 1 0 0 1 0 -32.14 cm BT /F35 10.91 Tf 0 0 Td[(Aufgab)-32(e)-298(R5.)]TJ/F15 10.91 Tf 78.37 0 Td[(\0505)-258(Punkte\051)-775(Es)-260(sei)]TJ/F18 10.91 Tf 89.17 0 Td[(C)]TJ/F15 10.91 Tf 11.39 0 Td[(der)-258(bin)]TJ 33.16 -0.47 Td[()]TJ 0 0.47 Td[(are)-258(zyklisc)27(he)-258(Co)-28(de)-258(der)-259(L)]TJ 114.58 -0.47 Td[()]TJ 0 0.47 Td[(ange)-259(7)-258(mit)-259(Generatorp)-26(olynom)]TJ/F18 10.91 Tf -326.67 -13.55 Td[(g)]TJ/F15 10.91 Tf 8.62 0 Td[(=)]TJ/F18 10.91 Tf 11.52 0 Td[(x)]TJ/F16 7.97 Tf 6.23 3.96 Td[(3)]TJ/F15 10.91 Tf 7.16 -3.96 Td[(+)]TJ/F18 10.91 Tf 10.91 0 Td[(x)]TJ/F15 10.91 Tf 8.66 0 Td[(+)-222(1,)-333(also)]TJ/F18 10.91 Tf 33.15 -16.93 Td[(C)]TJ/F15 10.91 Tf 11.6 0 Td[(=)]TJ/F21 10.91 Tf 11.52 0 Td[(f)]TJ/F15 10.91 Tf 7.27 0 Td[(\050)]TJ/F18 10.91 Tf 4.24 0 Td[(c)]TJ/F19 7.97 Tf 4.72 -1.64 Td[(i)]TJ/F15 10.91 Tf 3.38 1.64 Td[(\051)]TJ/F16 7.97 Tf 4.25 4.5 Td[(6)]TJ/F19 7.97 Tf 0 -7.2 Td[(i)]TJ/F16 7.97 Tf 2.88 0 Td[(=0)]TJ/F21 10.91 Tf 16.17 2.7 Td[(j)]TJ/F24 10.91 Tf 7.88 18.65 Td[(")]TJ/F16 7.97 Tf 12.12 -5.01 Td[(6)]TJ/F24 10.91 Tf -5.76 -3.28 Td[(X)]TJ/F19 7.97 Tf 1.03 -23.45 Td[(i)]TJ/F16 7.97 Tf 2.88 0 Td[(=0)]TJ/F18 10.91 Tf 13.67 13.09 Td[(c)]TJ/F19 7.97 Tf 4.72 -1.64 Td[(i)]TJ/F18 10.91 Tf 3.38 1.64 Td[(x)]TJ/F19 7.97 Tf 6.23 4.5 Td[(i)]TJ/F24 10.91 Tf 3.38 14.15 Td[(#)]TJ/F19 7.97 Tf 6.37 -33.33 Td[(x)]TJ/F17 5.98 Tf 4.76 2.27 Td[(7)]TJ/F22 7.97 Tf 4.16 -2.27 Td[( )]TJ/F16 7.97 Tf 6.58 0 Td[(1)]TJ/F15 10.91 Tf 2.31 14.68 Td[(=)-444([)]TJ/F18 10.91 Tf 16.36 0 Td[(g)]TJ/F21 10.91 Tf 8.02 0 Td[()]TJ/F18 10.91 Tf 5.46 0 Td[(h)]TJ/F15 10.91 Tf 6.28 0 Td[(])]TJ/F19 7.97 Tf 3.03 -2.36 Td[(x)]TJ/F17 5.98 Tf 4.77 2.26 Td[(7)]TJ/F22 7.97 Tf 4.15 -2.26 Td[( )]TJ/F16 7.97 Tf 6.59 0 Td[(1)]TJ/F15 10.91 Tf 12 2.36 Td[(f)]TJ 3.64 -0.48 Td[()]TJ -0.3 0.48 Td[(ur)-332(ein)]TJ/F18 10.91 Tf 31.54 0 Td[(h)]TJ/F21 10.91 Tf 9.32 0 Td[(2)]TJ/F30 10.91 Tf 10.3 0 Td[(Z)]TJ/F16 7.97 Tf 7.27 -1.64 Td[(2)]TJ/F15 10.91 Tf 4.73 1.64 Td[([)]TJ/F18 10.91 Tf 3.03 0 Td[(x)]TJ/F15 10.91 Tf 6.24 0 Td[(])]TJ/F21 10.91 Tf 4.85 0 Td[(g)]TJ/F18 10.91 Tf 5.45 0 Td[(:)]TJ/F15 10.91 Tf -378.72 -24 Td[(Die)-333(Dimension)-333(v)28(on)]TJ/F18 10.91 Tf 94.3 0 Td[(C)]TJ/F15 10.91 Tf 12.22 0 Td[(ist)-478(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)]TJ ET 435.12 -41.69 32.88 0.4 re f 435.12 -57.47 0.4 15.78 re f 467.6 -57.47 0.4 15.78 re f 435.12 -57.87 32.88 0.4 re f 1 0 0 1 0 -74.89 cm BT /F15 10.91 Tf 0 0 Td[(Die)-333(Anzahl)-333(der)-332(Co)-28(dew)27(orte)-333(in)]TJ/F18 10.91 Tf 143.24 0 Td[(C)]TJ/F15 10.91 Tf 12.22 0 Td[(ist)-435(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)]TJ ET 435.12 12.79 32.88 0.4 re f 435.12 -2.99 0.4 15.78 re f 467.6 -2.99 0.4 15.78 re f 435.12 -3.39 32.88 0.4 re f 1 0 0 1 0 -20.41 cm BT /F15 10.91 Tf 0 0 Td[(Die)-333(Minimaldistanz)-332(v)28(on)]TJ/F18 10.91 Tf 117.79 0 Td[(C)]TJ/F15 10.91 Tf 12.21 0 Td[(ist)-502(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)]TJ ET 435.12 12.79 32.88 0.4 re f 435.12 -2.99 0.4 15.78 re f 467.6 -2.99 0.4 15.78 re f 435.12 -3.39 32.88 0.4 re f 1 0 0 1 0 -20.41 cm BT /F15 10.91 Tf 0 0 Td[(\0501)]TJ/F18 10.91 Tf 9.7 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(1)]TJ/F18 10.91 Tf 5.45 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(0)]TJ/F18 10.91 Tf 5.45 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(0)]TJ/F18 10.91 Tf 5.46 0 Td[(;)]TJ/F15 10.91 Tf 4.84 0 Td[(0)]TJ/F18 10.91 Tf 5.46 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(0)]TJ/F18 10.91 Tf 5.45 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(0\051)-333(wird)-332(deco)-29(diert)-332(als)-629(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-162(.)-161(.)-162(.)-162(.)]TJ ET 350.57 12.79 117.42 0.4 re f 350.57 -2.99 0.4 15.78 re f 467.6 -2.99 0.4 15.78 re f 350.57 -3.39 117.42 0.4 re f 0 -13.55 468 0.5 re f 1 0 0 1 0 -32.14 cm BT /F35 10.91 Tf 0 0 Td[(Aufgab)-32(e)-384(R6.)]TJ/F15 10.91 Tf 80.39 0 Td[(\0505)-334(Punkte\051)]TJ -80.39 -16.39 Td[(Es)-465(sei)-466(\050)]TJ/F18 10.91 Tf 38.29 0 Td[(V)-56(;)-166(E)]TJ/F15 10.91 Tf 20.5 0 Td[(\051)-464(der)-464(Baum)-465(mit)-464(der)-464(Knotenmenge)]TJ/F18 10.91 Tf 175.16 0 Td[(V)]TJ/F15 10.91 Tf 14.21 0 Td[(=)]TJ/F21 10.91 Tf 13.9 0 Td[(f)]TJ/F15 10.91 Tf 5.45 0 Td[(1)]TJ/F18 10.91 Tf 5.46 0 Td[(;)-166(:)-167(:)-166(:)-333(;)]TJ/F15 10.91 Tf 26.06 0 Td[(6)]TJ/F21 10.91 Tf 5.45 0 Td[(g)]TJ/F15 10.91 Tf 10.53 0 Td[(und)-463(dem)-464(Pr)]TJ 60.31 -0.47 Td[()]TJ -0.3 0.47 Td[(uferco)-27(de)-465(\0502)]TJ/F18 10.91 Tf 54.8 0 Td[(;)]TJ/F15 10.91 Tf 4.84 0 Td[(3)]TJ/F18 10.91 Tf 5.46 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(3)]TJ/F18 10.91 Tf 5.45 0 Td[(;)]TJ/F15 10.91 Tf 4.85 0 Td[(2\051.)]TJ -455.27 -16.91 Td[(Geb)-27(en)-334(Sie)-333(die)-332(Nac)27(h)28(barn)-332(v)28(on)-332(3)-334(an,)-332(also)-334(die)-333(Menge)]TJ/F21 10.91 Tf 241.07 0 Td[(f)]TJ/F18 10.91 Tf 5.46 0 Td[(a)]TJ/F21 10.91 Tf 8.8 0 Td[(2)]TJ/F18 10.91 Tf 10.3 0 Td[(V)]TJ/F21 10.91 Tf 11.82 0 Td[(j)-277(f)]TJ/F18 10.91 Tf 11.51 0 Td[(a;)]TJ/F15 10.91 Tf 10.62 0 Td[(3)]TJ/F21 10.91 Tf 5.45 0 Td[(g)-278(2)]TJ/F18 10.91 Tf 18.79 0 Td[(E)]TJ/F21 10.91 Tf 8.68 0 Td[(g)]TJ/F15 10.91 Tf 5.46 0 Td[(.)]TJ ET 350.57 -20.51 117.42 0.4 re f 350.57 -36.29 0.4 15.78 re f 467.6 -36.29 0.4 15.78 re f 350.57 -36.69 117.42 0.4 re f 0 -46.85 468 0.5 re f 1 0 0 1 159.91 -66.06 cm BT /F35 10.91 Tf 0 0 Td[(Aufgab)-32(en)-383(mit)-385(L)]TJ 87.42 -0.55 Td[()]TJ 0 0.55 Td[(osungsw)32(eg)]TJ ET -159.91 -11.33 468 0.5 re f 1 0 0 1 -159.91 -29.93 cm BT /F35 10.91 Tf 0 0 Td[(Aufgab)-32(e)-384(L1.)]TJ/F15 10.91 Tf 78.53 0 Td[(\0508)-333(Punkte\051)]TJ -78.53 -19.22 Td[(Die)-257(F)83(olge)-257(\050)]TJ/F18 10.91 Tf 51.07 0 Td[(a)]TJ/F19 7.97 Tf 5.76 -1.63 Td[(n)]TJ/F15 10.91 Tf 5.64 1.63 Td[(\051)]TJ/F19 7.97 Tf 4.24 -1.73 Td[(n)]TJ/F22 7.97 Tf 5.14 0 Td[(2)]TJ/F31 7.97 Tf 5.65 0 Td[(N)]TJ/F17 5.98 Tf 5.75 -1.11 Td[(0)]TJ/F15 10.91 Tf 7.46 2.84 Td[(sei)-258(rekursiv)-256(de\014niert)-256(durc)29(h)]TJ/F18 10.91 Tf 128.13 0 Td[(a)]TJ/F16 7.97 Tf 5.77 -1.63 Td[(0)]TJ/F15 10.91 Tf 7.76 1.63 Td[(=)-278(1,)]TJ/F18 10.91 Tf 22.98 0 Td[(a)]TJ/F16 7.97 Tf 5.76 -1.63 Td[(1)]TJ/F15 10.91 Tf 7.76 1.63 Td[(=)-278(1)-257(und)]TJ/F18 10.91 Tf 40.77 0 Td[(a)]TJ/F19 7.97 Tf 5.77 -1.63 Td[(n)]TJ/F15 10.91 Tf 8.66 1.63 Td[(=)]TJ/F18 10.91 Tf 11.52 0 Td[(a)]TJ/F19 7.97 Tf 5.76 -1.63 Td[(n)]TJ/F22 7.97 Tf 5.14 0 Td[( )]TJ/F16 7.97 Tf 6.59 0 Td[(1)]TJ/F15 10.91 Tf 5.5 1.63 Td[(+)-69(2)]TJ/F18 10.91 Tf 16.52 0 Td[(a)]TJ/F19 7.97 Tf 5.76 -1.63 Td[(n)]TJ/F22 7.97 Tf 5.14 0 Td[( )]TJ/F16 7.97 Tf 6.59 0 Td[(2)]TJ/F21 10.91 Tf 7.76 1.63 Td[(2)]TJ/F30 10.91 Tf 10.3 0 Td[(Q)]TJ/F15 10.91 Tf 11.3 0 Td[(f)]TJ 3.63 -0.47 Td[()]TJ -0.3 0.47 Td[(ur)]TJ/F18 10.91 Tf 13.14 0 Td[(n)]TJ/F21 10.91 Tf 9.58 0 Td[()]TJ/F15 10.91 Tf 11.51 0 Td[(2.)]TJ -459.51 -16.38 Td[(Bestimmen)-307(Sie)-306(mit)-306(Hilfe)-305(der)-306(erzeugenden)-305(F)83(unktion)-303(die)-306(explizite)-306(Darstellung)-304(der)-306(F)84(olgenglieder)]TJ/F18 10.91 Tf 448.82 0 Td[(a)]TJ/F19 7.97 Tf 5.76 -1.64 Td[(n)]TJ/F15 10.91 Tf 5.64 1.64 Td[(.)]TJ ET 0 -49.15 468 0.5 re f 1 0 0 1 0 -67.74 cm BT /F35 10.91 Tf 0 0 Td[(Aufgab)-32(e)-384(L2.)]TJ/F15 10.91 Tf 78.53 0 Td[(\0508)-333(Punkte\051)]TJ -78.53 -16.39 Td[(Es)-230(sei)]TJ/F18 10.91 Tf 28.91 0 Td[(')]TJ/F15 10.91 Tf 9.63 0 Td[(die)-229(eulersc)28(he)]TJ/F18 10.91 Tf 61.75 0 Td[(')]TJ/F15 10.91 Tf 7.14 0 Td[(-F)83(unktion.)-407(Bestimmen)-230(Sie)-229(alle)-229(ungeraden)-227(nat)]TJ 212.74 -0.47 Td[()]TJ -0.31 0.47 Td[(urlic)28(hen)-228(Zahlen)]TJ/F18 10.91 Tf 75.03 0 Td[(n)]TJ/F15 10.91 Tf 9.05 0 Td[(mit)]TJ/F18 10.91 Tf 18.86 0 Td[(')]TJ/F15 10.91 Tf 7.13 0 Td[(\050)]TJ/F18 10.91 Tf 4.25 0 Td[(n)]TJ/F15 10.91 Tf 6.55 0 Td[(\051)-277(=)-278(6.)]TJ -440.73 -13.55 Td[(F)]TJ 7.42 -0.47 Td[()]TJ -0.3 0.47 Td[(ur)-243(w)28(elc)27(he)-244(dieser)]TJ/F18 10.91 Tf 76.59 0 Td[(n)]TJ/F15 10.91 Tf 9.2 0 Td[(ist)-244(die)-244(prime)-243(Restklassengrupp)-27(e)]TJ/F30 10.91 Tf 151.7 0 Td[(Z)]TJ/F22 7.97 Tf 7.28 3.96 Td[()]TJ/F19 7.97 Tf 0 -6.65 Td[(n)]TJ/F15 10.91 Tf 8.29 2.69 Td[(zyklisc)27(h?)-414(Geb)-27(en)-244(Sie)-244(jew)28(eils)-244(alle)-244(erzeugenden)]TJ -260.18 -13.54 Td[(Elemen)27(te)-334([)]TJ/F18 10.91 Tf 50.76 0 Td[(a)]TJ/F15 10.91 Tf 5.76 0 Td[(])]TJ/F19 7.97 Tf 3.03 -1.64 Td[(n)]TJ/F15 10.91 Tf 9.28 1.64 Td[(dieser)-333(Grupp)-26(e)-333(an.)]TJ ET 0 -54.2 468 0.5 re f endstream 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