Let $P(x)$ be a nonconstant polynomial whose coefficients are positive integers. If $P(n)$ divides $P(P(n) - 2015 )$ for every natural number n, then prove that $$P (-2015) = 0$$
I've observed that the proof depends on $ P(n)$ divides $ P(P(n)-2015)-P(-2015)\,$ but I cannot see how to prove that. Could someone please elaborate on how to proceed.