A Conjecture Concerning the Pure Exponential Diophantine Equation a^x+b^y=c^z

作     者：Mao Hua LE 

作者机构：Department of Mathematics Zhanjiang Normal College Zhanfiang 524005 P. R. China 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2005年第21卷第4期

页      面：943-948页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by the National Natural Science Foundation of China(No.10271104) the Guangdong Provincial Natural Science Foundation(No.011781) the Natural Science Foundation of the Education Department of Guangdong Province(No.0161) 

主　　题：Pure exponential diophantine equation Number of solutions Completely determine 

摘      要：Let a, b, c, r be fixed positive integers such that a^2 ＋ b^2 = c^r, min（a, b, c, r） 〉 1 and 2 r. In this paper we prove that if a ≡ 2 （mod 4）, b ≡ 3 （mod 4）, c 〉 3.10^37 and r 〉 7200, then the equation a^x ＋ b^y = c^z only has the solution （x, y, z） = （2, 2, r）.