Osnovy teorii Galua.

~.-Ypaotienue Huoatfaopa21.211

a n10TOmy a (14 3HatIHT BQQ6Ltte H4KaKoe 'IHCJAO) He m0oKeT 6wm~ nepBoo6 -pa3Hb1M KOPHem CpaBJeHHH5

(4.14)

X" (') 1 (mod m),

14 Mbl HpHXOJAHM K Teopeme:
XXIX. qT4c~no m HimeeT Hep~oo6pa3Hbe KOPHF1 B
TOJ~bKo B CaeaJyRoM1HX caiyusix:
10. M-P == rae p HeqeTrFoe Inpoc~oe 'rHCJIO,
20. m =2p V r~e p HeqeT~oe npoc~oe IIHCJIO,
30
3.m =.
B 3THX cnTyqag1x rnicao nepBoo6pa3Hblx KOpHefl paBHO
p(M).
~ 5. YpaB~eHne nHiiaropa.

CJeaLpoLLmx H

1. YpaBHeHflem HH4Jcaropa Ha3b1BaeT Cq ypaBHeHHe
(5.1) 2+ 2 )
B KOTOPOM He143~CTbie BupawaKlOT co6ofl aJLlHHbl KaTeTOB H MHHOTelHy3bl
flpAMOyrOJnbHor'O TpeyroJIbHHiKa. HTQ6bI lojiyLH4Tb camoe o6ulee BbipaKeH~e
21t15 HeH3BeCTHbIX, jaiottee Bce BO3MO)KHbie pau~o,,-aJ~bHbie pewneHH51 ypaB..
HeHH51 (5.1), nepernimem ypaBneffi~e (5. 1) Ta K:
x y
OTCio~aa cJneJyeT, 'ITO tiaCTHbIe 14 H MONKHO chieJ~ytoUtHm o6pa3om
BbIpa3HTb 'Iepe3 rlapameTp:
x y
- = COS CL) — =sin cx.
z ' z

Ho BeJIH'iHHbl Cos aL i sin or. MOrYT 6bITb paLU4OHaJ~bHO Bbipa)KeHbi 'lepe3
tg 7-~- a tg 2~ B cBoio otiepeJ~b paLLHOHahlbHO BbLpa)KaeTC51 4epe cs CO M H
sin ct:
a -Cosx z -x
tl= t

1 -tg 2
x _ 1-u2
z lA-t2'

CL= 2 tga-~
1aAI
-y 2u
Z 1~2 *

OTKy~aa

OTCIojAa., BBO)JIR K03qJ41HILWHT nlpOHQPaHOHajibHOCTVI V, MhI HPHXOJU4im
K camb1M O6JuIM rnapameTpIILec Hm Bh1payKeHHiim JIWI5I x, YV,
(5.2) x =(1- U2)V, y ==2uv, Z =(1~U2) V.