论文标题
在指数二苯胺方程$（n-1）^{x}+（n+2）^{y} = n^{z} $
On the exponential Diophantine equation $(n-1)^{x}+(n+2)^{y}=n^{z}$
论文作者
论文摘要
假设$ n $是一个积极的整数。在本文中，我们表明指数二磷酸方程$$（n-1）^{x}+（n+2）^{y} = n^{z}，\ n \ geq 2，\ xyz \ neq 0 $ $证明的主要工具是贝克的理论和Bilu-Hanrot-Voutier在Lucas数字的原始分歧上的结果。
Suppose that $n$ is a positive integer. In this paper, we show that the exponential Diophantine equation $$(n-1)^{x}+(n+2)^{y}=n^{z},\ n\geq 2,\ xyz\neq 0$$ has only the positive integer solutions $(n,x,y,z)=(3,2,1,2), (3,1,2,3)$. The main tools on the proofs are Baker's theory and Bilu-Hanrot-Voutier's result on primitive divisors of Lucas numbers.
