关于Diophantine方程(n+1)+(n+2)~y=n^z

On the Diophantine equation(n + 1) +(n + 2)~y = n^z

设n是正整数.本文证明了:方程(n+1)+(n+2)y=nz仅当n=3时有正整数解(y,z)=(1,2).

Let n be a positive integer. In this paper we prove that the equation （n ＋ 1） ＋ （n ＋ 2）^y = n^z only when n = 3 has the positive integer solution（n, y, z） = （3, 1, 2）.