Osnovy teorii Galua.

186

186 ~~~V. Ypaeutenuz e 3adaHmblmu opynna'Au

HlyCm X1, X2,... XI, - VOPRH no0JHH0ma'C, G~(X). HlOXCTaBJH9,q B (5.14)
x = x, (i = 1, 2, n.. ii nepe~k owawi noiyqaembwe 4OpmyJabi, 6yJaem
HlMemb:
x, -x... x, - ==n' nn+ )n -1,Q.)
Hlycm Teniepb yi' Y2, *.,y,,_I 6y~jyT KOPHH noJIn4mo a Gn-1 (x). Hjoxt.
CTaB 9,951 B (5.15) y = yj(i= 1, 2, n.. t-I1) ti nepeMuowaff noayqaembie
4)OPMyJlbI, IIOJIy4qHM:
K~pome TOMO, B cimyI cpopmyJabi (1. 10) I'JaBbI II ~ x4eTHOCTH MlHcal n(n -1
mMi Hmeem:,
OTKy~ta
I?(G0, Gon-I (..) 2 ntz-1 (ni 1) 2n-3(n - 2)2n-5.352 (C)0.
3jiecb
G,(x) x -2, G(X)-=X2-6x — 6,
OTxy~aa
R(0J2, GO) =G2(2) = 2,
H mbM nflOyqaem
nz(n - 1
R(G~, Gc1) (- ) 2 nn'1. (n - 1)2n - (ni - 2)2n-.. 35 23.
flpHHHmafT BO BHHmaHHe, 'ITO XI -X2. X,, = (ni + 1)!, noJny'iHm antii D
cme~aytouee Bblpa)KeHHe:
(n-fI)!n(ni+ 1)n1.n2n 2 (n - 1)2l4.34.22.
3TO 'HcJIo eCTb T(AtHbIA KBa~LpaT B ALBYX cayiya~ix: 1) ec~l im nCTb HeqtHmoe 'iHCqno, 2) ecJIH ni + 1 eCTb TO4Hbl1fA KBaJ~paT.
TaKHM o6j-Yaaom npiH BCSIKOM ti, KfPOMe cniyqai it = 4k + 2, MOMMFO nOCTPOHTb Bnojine onpueneHHeUMw o6paaoM ypaBHeHHH, rpynna raniya KOTOPWX
eCTb 3HKnvmHa rpyrrna.
Y iip a )He iH e 46. AToKa3arb IenI)HB0UUHM~CTb yPaB3HCHJI5 (5.1) Auris caryqaeB
fl = 9 HI n = 10.
Y n p a Nc t e H H e 47. HaH'TH JAHCKpHMHHIHTbl JLJISI Orp'l3KOB 4)YHKLLWI sin X H
~ 6.,KBajxpHpyembie JayHioqJH".
1. Etae B.tpeBHOCTH FI~rIIOKpaTOM 6bino o6Hapy,-,eHo, t'HO B tieKOTO~bMX
Cnyqa~5x nhIaotuAH l Hp [O qeKi"I T. e. 4rnryp, orpaHH'eiiHbix JLBYMH ayraMH
KpyroB., HmeIOT 3HaqeHIuff, aare6paH'IecK(H BbipaKaembie tiepe3 BXOAfu~iUeH B HX