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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 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 29 /notapproxequal put
dup 78 /N put
dup 81 /Q put
dup 90 /Z put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (1.100) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 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 0 /.notdef put
readonly def
/FontBBox{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMR12
%!PS-AdobeFont-1.1: CMR12 1.0
%%CreationDate: 1991 Aug 20 16:38:05
% 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 (CMR12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMR12 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 0 /.notdef put
readonly def
/FontBBox{-34 -251 988 750}readonly def
/UniqueID 5000794 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX12
%!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 /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 0 /.notdef put
readonly def
/FontBBox{-53 -251 1139 750}readonly def
/UniqueID 5000769 def
currentdict end
currentfile eexec
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3144 y(\(c\))49 b(Sei)41 b Fd(n)g Fa(2)g Fc(Z)p Fe(.)g(Zeigen)g(Sie,)g
(da\031)f Fd(n)g Fe(genau)h(dann)f(in)h Fc(Z)2815 3159
y Fb(p)2895 3144 y Fe(in)m(v)m(ertierbar)h(ist,)782 3264
y(w)m(enn)34 b Fd(n)f Fe(nic)m(h)m(t)h(durc)m(h)g Fd(p)e
Fe(teilbar)h(ist.)1274 b(\(6\))394 3468 y(39.)90 b(\(a\))48
b(Zeigen)e(Sie,)g(da\031)f(das)h(Hauptideal)g Fd(p)p
Fc(Z)2314 3483 y Fb(p)2399 3468 y Fe(v)m(on)g Fc(Z)2662
3483 y Fb(p)2702 3468 y Fe(,)g(das)f(v)m(on)h Fd(p)g
Fe(erzeugt)782 3588 y(wird,)34 b(das)f(einzige)g(maximale)h(Ideal)f(v)m
(on)g Fc(Z)2458 3603 y Fb(p)2531 3588 y Fe(ist.)782 3708
y(\(Hin)m(w)m(eis:)i(Zeigen)e(Sie)g(insb)s(esondere,)i(da\031)d(dieses)
j(Ideal)e(maximal)g(ist.\))603 3870 y(\(b\))49 b(Ist)33
b Fd(q)k Fe(eine)c(v)m(on)h Fd(p)e Fe(v)m(ersc)m(hiedene)k(Primzahl,)e
(so)f(ist)g Fc(Z)2801 3885 y Fb(p)2869 3870 y Fc(\035)28
b(Z)3040 3885 y Fb(q)3078 3870 y Fe(.)332 b(\(4\))394
4074 y(40.)49 b(Sei)33 b Fd(a)28 b Fa(2)g Fc(Z)964 4089
y Fb(p)1004 4074 y Fe(.)k(Zeigen)h(Sie,)h(da\031)e Fd(a)g
Fe(genau)h(dann)g(eine)g(rationale)g(Zahl)f(ist,)h(w)m(enn)568
4194 y(die)40 b Fd(p)p Fe(-adisc)m(he)h(Darstellung)g(v)m(on)f
Fd(a)g Fe(p)s(erio)s(disc)m(h)i(ist.)e(Dab)s(ei)g(b)s(edeutet)3319
4254 y(")3364 4194 y(p)s(eri-)568 4314 y(o)s(disc)m(h)-7
b(\\)7 b(,)29 b(da\031)f(nac)m(h)i(einer)f(gewissen)i(Zahl)d(v)m(on)h
(Stellen,)h(der)f(sog.)g(V)-8 b(orp)s(erio)s(de,)568
4435 y(ein)33 b(Blo)s(c)m(k)g(v)m(on)g(Stellen)h(k)m(omm)m(t,)g(der)f
(sic)m(h)h(danac)m(h)f(immer)h(wiederholt.)568 4555 y(\(Hin)m(w)m(eis:)
41 b(Zeigen)e(Sie,)g(zu)1602 4559 y(\177)1602 4555 y(ac)m(hst,)h
(da\031)f(sie)g(annehmen)h(k)2749 4559 y(\177)2749 4555
y(onnen,)g(da\031)e Fd(a)h Fe(nic)m(h)m(t)568 4676 y(durc)m(h)j
Fd(p)f Fe(teilbar)h(ist.)g(Zeigen)g(Sie)g(dann,)f(da\031)g(p)s(erio)s
(disc)m(he)j(Zahlen)d(rational)568 4796 y(sind,)d(und)f(v)m(ersuc)m
(hen)j(sie)e(daraus)f(die)h(Umk)m(ehrung)g(zu)g(ersc)m(hlie\031en.)h
(Beac)m(h-)568 4916 y(ten)33 b(Sie)g(T)-8 b(eil)33 b(b\))g(v)m(on)g
(Aufgab)s(e)g(38.\))1492 b(\(6\))324 5120 y(Abgab)s(e:)37
b(Dienstag,)h(1.7.2003,)e(11.00)h(Uhr,)2063 5098 y(\177)2051
5120 y(Ubungsk)2424 5124 y(\177)2424 5120 y(asten)j(im)d(1.)h(Sto)s(c)m
(k)g(des)g(Ma-)324 5240 y(thematisc)m(hen)d(Instituts.)324
5360 y(Bitte)e(geb)s(en)g(Sie)g(auf)f(Ihrer)h(L)1475
5364 y(\177)1475 5360 y(osung)g(Ihren)h(Namen)f(und)g(Ihre)2753
5339 y(\177)2741 5360 y(Ubungsgrupp)s(e)h(an.)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF