# Previous year Olympiad problem (polynomials) [duplicate]

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.