Osnovy teorii Galua.

~3. Paapewuumbie opynnulb u ypaunenuq 3

1 131

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T. e. paapeummbe ypaBueHHi5i.
13. BeumeCTBe~bibe paaH~aJnbl. Eliue CO Bpemerni OTKPblTHRl peuieHRni
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IKol-Ja Ky6H~ecKoe ypaaiieH-me HtmeeT Bce Beu4eCTBeHlibIe KOPHII, paJxiKaubHoe
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HJHKaK He y~a~auioCb li36aBHTbCS. BB BHJ9 BToro paccmaTpHiBaembift Cntyqaiaf
flonTyLIHn HII3BaHHe c a sus i r re du c ib ii S, T. e. HenpHBO.LIHMoro Ciy'ias.
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Teopema 70. EcJil B ypaBHeHHH4
(3.33) f(x)= ---0
BCe KOPHH BeLLeCTBeHHbJ, a HOP,9ULOK rpynirbi coJLep)KHT HetieTrrbe fnpoCTbie MH0)KHTeJIH, TO ero KOPHH4 He MOrYT 6wlTb Bblpa)KeHbl 'iepe3
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rpyrrna ypaBHeH5ig (3.33) floHHiaeTC5B, ecuin mbl [IpHCOeJiHHM K o6JnaCTH
paLWOHaJ~bHOCTH HppaBLLFOHaJIbHOCTb J/a, i-je a BeeT~Ho qHCJIO H p npoCToe qtiHcjlo. Torxaa no Teopeme 63 3Toro we noFIH}eHI4I MO)KHO JLOCTHrHyTI-,
nHHcoeILHHflfl K o6JnaCTH paiJHOHaJbHOCTH BeJiH'IHly (ja) nonw K(1(a)
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c iieft BeJ1H4HHbl.lie)aT B noue K(xl, X2,., X,,) Hi nOTOMY BeLIieCTBeHHbI.
4~OnpIxel)KlbIMH Cp (a) BeJ1HqHHaMH H1BJARIOTCH BehIqjH'IHI
P 2 2n - 2 it..
ut =e CO S - +tisin -, e == cos - -sin - (cm. ~ 1). Bce~
p p p
BeA1HMHHbi (3A34), coruaCHo YCJIOBHI-O, BemieCT~eH~~i, a nIOTOMY OHH He MCHRIOTC'i IpH rnepexoiae ic coripmiKeHHo-KomnaeKCHbIM BeJIH'IHHaM, T. e. nmeeT
me CTO
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$,coitepmaetel nlQLCTaHOBKY 2 rae S = SEf~. oTlcia
riopiaoK n1OJCTaHOBKHi S He'IeTHblfl (SP 1), To rpyrina k) Aouo)ua Tai~ie
couiepwar'b flOJCTaH-OBKY S. TaKHM o6pa3oM Ben~'HqHa p xtornIWa Bbip3)KaTbCfl
4epe3 p-e KOPHH H3 eJIHHHbl~h, T. e. yAOBJIeTBOpfITL HeFHPHBOJAHMOMY ypaBHeHHIO, CTeIneHB KOTOporo eCTb aLenlHTeJnb '4HcJa p -,a noToMy He mo)KeT
IIOHH3HTb rpynny ypaBHeHH5I (3.3 3) B p paa.