Let
![b,n > 1](/media/m/8/f/d/8fd1a47095c6ca01069e57312aebf286.png)
be integers. Suppose that for each
![k > 1](/media/m/e/a/0/ea0d9143b264f0f11e7f6efe66f19a42.png)
there exists an integer
![a_k](/media/m/8/f/f/8ffe60c23d3334cc61d0660473bf1b61.png)
such that
![b - a^n_k](/media/m/c/8/7/c87ba6b4503449a89d9b224e5d637c19.png)
is divisible by
![k.](/media/m/3/5/d/35d6ded5ad555e4f371e82635560eb35.png)
Prove that
![b = A^n](/media/m/0/a/3/0a3750ddaa8f75efb83b44d416b00518.png)
for some integer
Author: unknown author, Canada
%V0
Let $b,n > 1$ be integers. Suppose that for each $k > 1$ there exists an integer $a_k$ such that $b - a^n_k$ is divisible by $k.$ Prove that $b = A^n$ for some integer $A.$
Author: unknown author, Canada