《费马大定理的简捷证明.docx》由会员分享，可在线阅读，更多相关《费马大定理的简捷证明.docx（2页珍藏版）》请在taowenge.com淘文阁网|工程机械CAD图纸|机械工程制图|CAD装配图下载|SolidWorks_CaTia_CAD_UG_PROE_设计图分享下载上搜索。
1、A Simple Proof of Fermats Last TheoremZengyong LiangFermat is a French justice and amateur mathematician .In 1637, Fermat was inadvertently attracted by the Pythagorean work described in the ancient Greek mathematician Diophantines arithmetic. He had a whim about whether he could find a solution to
2、the indefinite equation of the Pythagorean equation.The original Pythagorean equation can be expressed as the search equation:xn+ yn zninteger solution of.Fermat then annotated in the book arithmetic1: it is impossible to divide a cubic number into two cubic numbers, a fourth power into two fourth p
3、owers, or generally divide a power higher than the second power into two powers of the same power. On this, I am sure I have found a wonderful proof. Unfortunately, the blank space here is too small to write down.H This problem is then called Termafs Last Theorem”.For more than three centuries, the
4、best mathematicians in history have tried to prove it, but got nothing. In 1994, Wiles indirectly proved Fermats theorem by using modern mathematical methods such as modular form, Gushan Zhicun conjecture and the properties of elliptic curves of Galois group. But his proof is 130 pages long and quit
5、e esoteric, which is obviously not the short proof Fermat said. People are still seeking a concise Fermafs theorem as Fermat saidIf x, y and z have common factor, we can eliminate them. Is that the equation becomes An+Bn=Cn.So, we can say that:Fermats last theorem: If equationAn+Bn=cnthere is no pos
6、itive integer solution.Proof. If equation (1) is true, et A=CB=C-bf thenAn= (CQ)11An=Cn - (?”%+.+( -7)+( 1) n Q n(2)Bn= QCb) nBn=Cn - 0%+.+(-1)+(一，)1(3)By (2)4- (3):An+Bn=2Cn - 。-1(+匕)+.+(-匕n-l)+(_/)n(n +匕 n)(4)Since An + Bn = Cn, thenCn=2Cn 0-1(。+/?)+.+(/) n/C(an/+/?n-l )+(1) n(n 十 n)by (4).SoCn -
7、n +/?)+.+( -7) n.C(n+ bn-1)+(-)n(an + bn)=0(5)By Theorem 1, we know that ifCn +(-7)nn =0 ,(6)where this asked C-q .Comparison (5) and (6), we get:If (5) is true, this asked :a +h=q=C;a2 +h2=q2=C2;+ bn =q n=Cn.This is impossible, then equation (5) is not true. Thus, the equation (1) is not true.Theorem 1. IfCn 一。一%+.+(-1)this asked C-q.Proof. Since(C q ) n = c n nC% + +( 一) n-nC q n-1 +(/) % n ,then the equation only holds if C=q.