Are there pairs $(x,n)$ for which :$x^n=0\bmod x+n$ with $x \neq n$ are positive integers?

Question

I have tried to find relationship for congruence between $x$ and it's power , such that I want know if there are pairs $(x,n)$ satisfying : $x^n=0\bmod (x+n)$ with $x, n$ are positive integers , then my question here is :

Question: Are there pairs $(x,n)$ for which :$x^n=0\bmod x+n$ with $x \neq n$ are positive integers?