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：Mao Hua LE 

机构地区：[1]Department of Mathematics, Zhanjiang Normal College, Zhanjiang 524048, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2008年第6期917-924,共8页数学学报（英文版）

基　　金：the National Natural Science Foundation of China (No.10271104);the Guangdong Provincial Natural Science Foundation (No.04011425)

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）.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）.

关 键 词：exponential diophantine equation positive integer solution generalized Fermat conjecture 

分 类 号：O156.4[理学—数学]