关于一类不定方程正整数解的问题  

On the Problem of an Positive Integral Solution of One Kind Indeterminate Equation

作　　者：李尚龙[1] 

机构地区：[1]渭南职业技术学院数理科学系,陕西渭南714000

出　　处：《怀化学院学报》2010年第5期31-33,共3页Journal of Huaihua University

基　　金：陕西省教育厅基金项目(09JK432)

摘　　要：利用初等数论知识推导并证明了不定方程1/a+1/b=1/c的正整数解的一般公式,并且推导出了不定方程1/a2+1/b2=1/c2的全部正整数解,并对不定方程1/an+1/bn=1/cn(n≥3)是否有正整数解做了讨论,解决了这一类不定方程的正整数解的问题.This paper used the knowledge of elementary number theory to deduce and prove the general formulas of positive integral solution to the indeterminate equation 1/a＋1/b=1/c.This paper also has deduced and afforded us to obtain all positive integral solution to the indeterminate equation 1/a2＋1/b2=1/c2,and has made a discussion if it has positive integral solution to indeterminate equation 1/an＋1/bn=1/cn（n≥3,n∈N＊）.Thus it has solved the problem to positive integral solution of the kind indeterminate equation.

关 键 词：不定方程 正整数解 初等数论 

分 类 号：O156.2[理学—数学]