Fermat大定理的较简证明  

Simple proof of Fermat last theorem

作　　者：聂钦汉 

机构地区：[1]西南民族大学,四川成都610041

出　　处：《西南民族大学学报（自然科学版）》2017年第3期307-313,共7页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：对任三个正整数x、y、z,证明了(x/z)~n+(y/z)~n≠1(n≥3的整数),进而证明了n次不定方程x^n+y^n=z^n(n≥3的整数)无正整数解.因为由任三个x、y、z组成的三数组有无限多个,把这些三数组分成五类,并对各类三数组证明都有(x/z)~n+(y/z)~n≠1.前三类x、y、z易证有(x/z)~n+(y/z)~n≠1,第四类x、y、z用无限整体与有限部份间的关系可证(x/z)~n+(y/z)~n≠1,第五类x、y、z,先引入N_小概念,又对N_小>3的x、y、z引入N_大概念,再用引2的结果证明N_小与N_大是相邻整数,于是可证(x/z)~n+(y/z)~n≠1,从而易证Fermat大定理正确.This paper prves the equation of （x/z）n＋（y/z）n≠1（ the integer of n ≥ 3） for any three positive integers x,y,z, and the equation of xn ＋ y＂ = zn （ the integer of n ≥ 3 ） without positive integer solution. Three arrays composed of any three x, y, z have infinite number, these three groups are divided into five categories, and all three groups prove the equation of （x/z）n＋（y/z）n≠1.For the first three categories x, y, z, it is easy to prove the equation of （x/z）n＋（y/z）n≠1.For the fourth category x, y, z, the equation of （x/z）n＋（y/z）n≠1 can be proved by the relationship between the infinite whole and finite part of the card. For the fifth category x,y, z, the equation of （x/z）n＋（y/z）n≠1 can be proved by firstly introducing the concept of Nsmall, and introducing the concept of Nlarge for the Nsmall 〉 3 x, y, z, and then proving that Nsmall and Nlarse are adjacent integers by citing the results of 2. Thus it is easy to prove that Fermat last theorem is correct.

关 键 词：整数 分数 小数 4k数 2n1数 N小 N大 

分 类 号：O156[理学—数学]