Osnovy teorii Galua.

198

798 ~~~~~~~~Teopuit tuceA

JeJ~eIHM lepB~iti OCTaTOIC Ha BTOpOfI OCTaTOK:
r,~-r2q2, + r3,
H T. aL. TaK KaK nlocJe2Ao1aTeqbHbie OCTaT]KH 13 C11JIY, I H1ayT Bce Bpem51 y6biBaRI TO npoutecc JLoAlxeH riocne KOHe4H~rO tuicza maroB o6opBaTbCfl, T. e.
OAK1H 113 OCTaTKOB JaojuweH- o6par1THcWI B Hy~ib: Tm-r Toriaa, KiK MM!
cejftiac atLOaweKm, Tm qBJI~ieTCf1 o6uiumm 11a16on'bwimM JuJTenem qiic~na a H1 b.
B camom XeAe, 113 riocuieiiero paBeHCTBa
a bq + r.,,
b qt+ r2,
(1.1) J~~~~~r r~ r2q2 j-r.,
I,- r~ qm~l ~ rm,
mb! 3aK.THoqaem, WIO Tml ae~j1HTCH ita Tm; aiajiee 113 ripeauiociiejiHero paBeHCTBa, B CHAY1 HI1 III Mbl 3aKJIIo'Iaem, 'ITO JL- aJI11TCSI Ha Tm; Hafl! TaK11M flyTem, Mb! flOCTefieHH~O JOKa)Kem, 'ITO rm-21 Tm -3' ** r 2, r, r, b, a.AeawRCH Ha Tn.
Teneph JLoi~a)em, 'ITO BCHK1Hft o6nt11 ejtil11Tehlb d qticeni a H b eCTb
TaK)Ke JteJIHTeJb q11caa r ~. ~JAhR 3TOCo, Ha'IHHasi C nepeoro paBeHCTBa, MbI
y6ew~aemcf, Wro r, = a-bq ael~JHT1 Ha d; aaTeM 113 B3TOporo paBeHCTBa
B14H~!M, qITo r2 = b-rlq1 aejJIHTC5I Ha d, 14 T. R.; HaKOHeIL, 113 npea7noc~neIL.
Hero paBeHCTBl cJae~iyeT, LITO r., JaeJ!HTC51 Ha d.
TaKHM o6pa3oM Bice o6uwee fig 1Temi!H '1ceJ a 11 51B.0 HJI!TC5I LeJIH4TeJ~l1MH1
qI11Ca~ Trn- OTKyILa cileJyeT, 'ITO rm lH3J1ReTC5I 06!ILlM HaiH6onblbuM ~aHe.TMeem
a Hi b.
JXUI! o6o3Ha'IeHul o6nmeFo Ha116OflbterO aiejnt~ensi 'I1ceJ a ii b nH~1H$T
cHmBoJI (a, 1).
4. V. Ec.im d eCTb o6uLtiil HaH6OJ~blln11A XLeJ11TeJlb qnceui a H b
TO ypaBneH~e
(1.2) ax +by -d
11meeT pewHIH151 B itejibIX qiuciiax.
]I 0 K a 3 a T e.7 b C T B o. H-olb3yl~Cb npeanociieauin palBeHCTBOM (11,MO)KHO
qbjpa3HTb d = rm qepe3 T,_ H11Tn~g
(1.3) Tm =Tm-2-Tm1 qmii
3aTeM Bbip31mm Tm1epe Tm-2 11 rm3: rT-1 Tm rn3rm-2 qm-2 11 noACTa BHM B (1. 3):.
rm: =T rn2 (1 +q_lqq-2) - rm q 1
IHpIoA~aoiaq flpoleLec, Bb1a331M Tm, qepeaT3 11rH m41 5 H T. IL.;
HaKoHell, qepea b H1 a. 0603Ha'Iasi nojlyqaembie npH1 13TOM K03Ci~t11HLHeHTbi niPi
a ti b qepe3 X 11 Y, MbM f!OJlyqHM peiuenne ypaBeffibl (2.1).