The number $m+n^2$ is divisible by $m+n$. Prove that the number $m+n^3$ is divisible by $m+n$. 
$m$ and $n$ are positive integer numbers; $m+n\mid m+n^2$.
  Prove that $m+n\mid m+n^3$

So far I have done:
If $m+n\mid m+n^2$, then $m+n\mid (m+n^2)-(m+n)=n^2-n=n(n-1)$.
$m+n^3=n(n^2-n)+(m+n^2)$ and each component is divisible by $m+n$
Proved, thanks for help!

Hint: If $m + n^2$ is divisible by $m + n$ then so is $(m + n^2) - (m + n) = n^2 - n$.
