关于指数Diophantine方程n^x+(n+2)~y=(n+1)~z

On the exponential diophantine equation n^x+(n+2)~y=(n+1)~z

设n是正整数.本文运用Gel’fond-Baker方法证明了:当n>3×1015时,方程nx+(n+2)y=(n+1)z无正整数解(x,y,z).

Let n be a positive integer. In this paper, using the Gel＇fond-Baker method, we prove that if n〉3×10^15,then the equation n^x＋（n＋1）^zhas no positive integer solution（x, y, z）.