Osnovy teorii Galua.

~7. Pa3petuwwbae epynnui

OHa HmieeiD rnopHAo 2 (p - 1)2. CO0TBeTCTByloaiau 9TOMY TilY rpyfnna3
HmeeT nfplOPJLK 2p2(p - 1)2.
IIT 1111. HIpoH3BoxiRflHe noAtCTaHoBKH:
rage p:* 0 (mod p) H p OAHO H 'P0 }Ke R5 Bcex HnJACTaH0BOK rpyflfbl. H~opHJXoK 9Tofl rpynflbl pa~eH 2(p2 - 1), a n1OTOMY nIOpBJOK COOTBeTCTByIOLLeft
rpyrlrbh %0 pa~eH 2p2(p2-1)
III T Ii i. 3,aecb HeofxoalHmo panhuw-ia caytiap p 1 --- I p ==3 (mod 4).
A) p 1 (mod 4). O603Haqaei tepe3 i KOpeHb cpaBHeHHH j2 _
(mod p), noAy4iim cjieapyonuie npOH3BOJ1~wL1ie noECTaHoBKH4:
B) p -=3 (mod 4). Pewnae cpaB~eHee s2 + t2 ~ 1 0 (mod p), nonyi4Hm
caieityiouuie HPOH3BOAL1JHm~ rnoJCTaHoBKH:
fIOP,9,40K S9THx rpy-nr pae B o6oHx caiyqaox 24(p - 1), a I1OTOMY
t1OPR1XOK COOTBeTCTBYIOIIefl rpynir~ WJ pa~eH 24 p2(p - 1).
HpuH P 3 HI p = 5 iimeeT meCTO H4cKJIoqeHHe, KOTOpoe COCTOHT B TOM,
WoT npH p = 3 rpynnbi flepBbIX AJBYX THnIOB H nIpH p = 5 rpynbim nepeoro
Tilna BXOJAHT B C0OTBeTCTB~ioL1LHe rpyflflbl Tpe~TberO Tilna, KaK JAeJIHTeJIH.