This question is an exact duplicate of:

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.


merged by Aloizio Macedo Oct 11 '18 at 15:56

This question was merged with If $P(n)$ divides $P(P(n)-2015)$, prove that $P(-2015)=0$ because it is an exact duplicate of that question.