关于不定方程a^x+b^y=c^z

On the Diophantine Equation a^x+b^y=c^z

设a,b,c都是大于1的正整数,而且(a,b)=(b,c)=(c,a)=1。考虑不定方程 a^x+b^y=c^z,x≥0,y≥0,z≥0的整数解。本文给出了方程当max(a,b,c)=15时的全部解,从而得到了当max(a,b,c)≤16时的全部解。

Let a, b, c be three integers greater than 1 and(a,b)=(b,c)=(c,a)=1. We have obtained all the non-negative integral solutions of those Dioph- antine eqauation a^x+b^y=c^z. in. which max(a,b,c)