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(Elemen)m(t)i(v)m(on)568 2291 y Fd(Z)637 2306 y Fc(p)674
2291 y Fh([)p Ff(x)p Fh(],)33 b(reduzib)s(el)f(ist.)568
2411 y(\(Hin)m(w)m(eis:)h(V)-8 b(erw)m(enden)34 b(Sie)f(Aufgab)s(e)f
(24)g(v)m(on)h(Blatt)f(6\).)721 b(\(6\))394 2614 y(30.)49
b(Sei)29 b Ff(p)h Fh(eine)g(ungerade)h(Primzahl.)e(F)1925
2618 y(\177)1922 2614 y(ur)h(eine)g(ganze)g(Zahl)f Ff(n)p
Fh(,)h(die)g(nic)m(h)m(t)g(durc)m(h)i Ff(p)568 2735 y
Fh(teilbar)f(ist,)h(de\014nieren)h(wir)f(das)h(Legendre-Sym)m(b)s(ol)
989 2896 y Fb(\022)1072 2969 y Ff(n)p 1072 3014 59 4
v 1077 3105 a(p)1140 2896 y Fb(\023)1241 3036 y Fh(:=)1372
2866 y Fb(\()1452 2968 y Fh(1)28 b(:)175 b Ff(n)28 b
Fe(\021)g Ff(m)2007 2932 y Fg(2)2146 2968 y Fh(\(mo)s(d)k
Ff(p)p Fh(\))h(f)2557 2972 y(\177)2554 2968 y(ur)f(ein)g
Ff(m)c Fe(2)g Fd(Z)1452 3113 y Fe(\000)p Fh(1)g(:)98
b Ff(n)28 b Fe(6\021)g Ff(m)2007 3076 y Fg(2)2146 3113
y Fh(\(mo)s(d)k Ff(p)p Fh(\))h(f)2557 3117 y(\177)2554
3113 y(ur)f(alle)f Ff(m)d Fe(2)g Fd(Z)568 3383 y Fh(Ist)j
Ff(n)g Fh(durc)m(h)h Ff(p)f Fh(teilbar,)f(so)h(sei)g(das)g
(Legendre-Sym)m(b)s(ol)2683 3273 y Fb(\020)2752 3344
y Fc(n)p 2752 3361 43 4 v 2756 3418 a(p)2805 3273 y Fb(\021)2892
3383 y Fh(=)d(0.)j(Zeigen)f(Sie:)609 3684 y(\(a\))782
3544 y Fb(\022)866 3617 y Ff(n)p 866 3661 59 4 v 871
3752 a(p)934 3544 y Fb(\023)1035 3684 y Fe(\021)e Ff(n)1198
3648 y Fg(\()p Fc(p)p Fa(\000)p Fg(1\))p Fc(=)p Fg(2)1498
3684 y Fh(\(mo)s(d)k Ff(p)p Fh(\))603 3973 y(\(b\))782
3832 y Fb(\022)866 3906 y Fe(\000)p Fh(1)p 866 3950 127
4 v 904 4041 a Ff(p)1002 3832 y Fb(\023)1103 3973 y Fh(=)27
b(\()p Fe(\000)p Fh(1\))1408 3937 y Fg(\()p Fc(p)p Fa(\000)p
Fg(1\))p Fc(=)p Fg(2)568 4234 y Fh(\(Hin)m(w)m(eis:)33
b(Beac)m(h)m(ten)h(Sie)e(den)h(kleinen)g(F)-8 b(ermatsc)m(hen)33
b(Satz.\))530 b(\(6\))394 4437 y(31.)49 b(Sei)21 b Ff(p)h
Fh(eine)f(ungerade)i(Primzahl.)d(Zeigen)h(Sie,)g(da\031)h(der)g
(Kreisteilungsk)3224 4441 y(\177)3224 4437 y(orp)s(er)f
Fd(Q)3541 4452 y Fc(p)568 4557 y Fh(genau)42 b(einen)h(quadratisc)m
(hen)g(Un)m(terk)2051 4561 y(\177)2051 4557 y(orp)s(er,)h(also)e(einen)
g(K)2893 4561 y(\177)2893 4557 y(orp)s(er)g(der)h(F)-8
b(orm)568 4678 y Fd(Q)11 b Fh(\()677 4593 y Fe(p)p 766
4593 51 4 v 766 4678 a Ff(d)p Fh(\))32 b(f)920 4682 y(\177)917
4678 y(ur)h(eine)f(quadratfreie)h(ganze)g(Zahl)e Ff(d)p
Fh(,)h(en)m(th)2579 4682 y(\177)2579 4678 y(alt.)568
4798 y(\(Hin)m(w)m(eis:)47 b(Beac)m(h)m(ten)i(Sie)e(Aufgab)s(e)g(28)g
(v)m(on)h(Blatt)e(7.)h(Betrac)m(h)m(ten)i(Sie)e(die)568
4919 y(Galoisgrupp)s(e)30 b(v)m(on)k Fd(Q)1418 4934 y
Fc(p)1499 4923 y Fh(\177)1496 4919 y(ub)s(er)f Fd(Q)12
b Fh(.\))1579 b(\(4\))p eop
%%Page: 2 2
2 1 bop 394 548 a Fh(32.)49 b(Sei)32 b Ff(\020)j Fe(2)28
b Fd(C)58 b Fh(eine)33 b(primitiv)m(e)d(f)1652 552 y(\177)1649
548 y(unfte)j(Einheitswurzel)f(und)1316 853 y Ff(\034)39
b Fh(:=)1582 728 y Fg(4)1528 758 y Fb(X)1533 967 y Fc(n)p
Fg(=1)1689 742 y Fb(\020)1758 785 y Ff(n)p 1758 830 59
4 v 1763 921 a Fh(5)1826 742 y Fb(\021)1902 853 y Ff(\020)1953
811 y Fc(n)2027 853 y Fh(=)28 b Ff(\020)h Fe(\000)22
b Ff(\020)2353 811 y Fg(2)2414 853 y Fe(\000)h Ff(\020)2565
811 y Fg(3)2626 853 y Fh(+)f Ff(\020)2775 811 y Fg(4)568
1153 y Fh(Zeigen)32 b(Sie:)609 1356 y(\(a\))48 b Ff(\034)835
1320 y Fg(2)903 1356 y Fh(=)27 b(5)603 1518 y(\(b\))49
b Fd(Q)12 b Fh(\()892 1436 y Fe(p)p 981 1436 49 4 v 981
1518 a Fh(5)o(\))28 b Fe(\032)g Fd(Q)1272 1533 y Fg(5)568
1722 y Fh(\(Hin)m(w)m(eis:)j(Die)f(De\014nition)f(v)m(on)j
Ff(\034)42 b Fh(l)1915 1726 y(\177)1915 1722 y(a\031t)30
b(sic)m(h)h(leic)m(h)m(t)g(auf)g(allgemeine)d(Primzah-)568
1842 y(len)34 b(v)m(erallgemeinern,)f(und)i(man)f(k)-5
b(ann)2109 1846 y(\177)2109 1842 y(ahnlic)m(h)34 b(zeigen,)h(da\031)f
(der)h(eindeutige)568 1963 y(quadratisc)m(he)26 b(Un)m(terk)1424
1967 y(\177)1424 1963 y(orp)s(er)h(v)m(on)f Fd(Q)1925
1978 y Fc(p)1996 1963 y Fh(der)g(K)2233 1967 y(\177)2233
1963 y(orp)s(er)g Fd(Q)11 b Fh(\()2593 1875 y Fb(p)p
2699 1875 507 4 v 2699 1963 a Fh(\()p Fe(\000)p Fh(1\))2901
1934 y Fg(\()p Fc(p)p Fa(\000)p Fg(1\))p Fc(=)p Fg(2)3156
1963 y Ff(p)p Fh(\))25 b(ist.\)\(4\))324 2191 y(Abgab)s(e:)32
b(Dienstag,)g(10.6.2003,)f(11.00)h(Uhr,)2088 2170 y(\177)2076
2191 y(Ubungsk)2449 2195 y(\177)2449 2191 y(asten)i(im)d(1.)h(Sto)s(c)m
(k)i(des)f(Ma-)324 2311 y(thematisc)m(hen)g(Instituts.)324
2432 y(Bitte)f(geb)s(en)h(Sie)f(auf)g(Ihrer)h(L)1475
2436 y(\177)1475 2432 y(osung)g(Ihren)h(Namen)e(und)h(Ihre)2753
2410 y(\177)2741 2432 y(Ubungsgrupp)s(e)h(an.)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF