Fermat大定理的初等证明  

Rudimentary Proof of Fermat's Last Theorem

作　　者：李高[1] 

机构地区：[1]山西大同大学煤炭工程学院,山西大同037003

出　　处：《河北北方学院学报（自然科学版）》2017年第7期1-5,10,共6页Journal of Hebei North University:Natural Science Edition

基　　金：山西大同大学教学改革资金资助项目(XJY2013211)

摘　　要：目的探寻费尔马大定理的初等证明。方法利用二项式定理展开式、代数方程根与系数的关系,及其初等数论的知识,采用反证的方法,用初等方法对费尔马大定理进行论证。结果费尔马大定理对任意的正整数n>2时,不定方程x^n+y^n=z^n没有正整数解。结论费尔马大定理可以用初等方法直接证明其结论的正确性。避弃了烦琐的间接初等证明法,避开了高深的高等解法,在学习和应用时给出了解决问题的思维方式和思路。Objective To explore the elementary proof of Fermat's Last Theorem.Methods The binomial theorem expansion,the relationship between root and coefficient of algebraic equation,and the elementary number theory are adopted to prove Fermat's Last Theorem with reduction to absurdity disproof and elementary method.Results For Fermat's Last Theorem with any positive integer n>2,indeterminate equation x^n+y^n=z^n has no positive integer solutions.Conclusion The elementary method of Fermat's Last Theorem can be used directly to prove the correctness of the conclusion,which abandons the cumbersome indirect elementary proof method and avoids the advanced higher solution.This provoking method gives the way of thinking and ideas to solve the problem in the study and application.

关 键 词：不定方程 正整数解 公因子 奇素数 费尔马小定理 费尔马大定理 

分 类 号：O156.2[理学—数学]