关于指数Diophantine方程(n+1)~x+(n+1)~y=n^z

On The Exponential Diophantine Equation (n+1)~x+(n+1)~y=n^z

设n是正整数,本文运用初等方法证明了:方程(n+1)x+(n+1)y=nz没有适合x>1的正整数解(x,y,z).

Let n be a positive integer with n〉1.In this paper, using some elementary methods, the equation （n＋1）^x＋（n＋1）^y=n^z has no positive integer solution （x,y,z） with x〉1 is proved.