关于Diophantine方程(44n)^(x)+(117n)^(y)=(125n)^(z)的整数解

On the integral solutions of Diophantine equation(44n)^(x)+(117n)^(y)=(125n)^(z)

在Jesmanowícz猜想的基础上,利用初等方法证明了对任意的正整数n,Diophantine方程(44n)x+(117n)y=(125n)z仅有正整数解(x,y,z)=(2,2,2).

In this paper, basing on Je′smanow′？cz′ conjecture, it is proved that for any positive integral n the Diophantine equation （44n）x＋（117n）y = （125n）z has only integral solution （x, y, z） = （2, 2, 2） by elementary method.