On the Diophantine System a^2+b^2=c^3 and a^x+b^y=c^z for b is an Odd Prime
On the Diophantine System a^2+b^2=c^3 and a^x+b^y=c^z for b is an Odd Prime作者机构：Department of Mathematics Zhanjiang Normal College Zhanjiang 524048 P. R. China
出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)
年 卷 期：2008年第24卷第6期
页 面：917-924页
核心收录：
学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学]
基 金：the National Natural Science Foundation of China (No.10271104) the Guangdong Provincial Natural Science Foundation (No.04011425)
主 题：exponential diophantine equation positive integer solution generalized Fermat conjecture
摘 要：Let a, b and c be fixed coprime positive integers. In this paper we prove that if a^2 ＋ b^2 = c^3 and b is an odd prime, then the equation a^x ＋ b^y = c^z has only the positive integer solution （x, y, z） = （2,2,3）.
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