Question 161
Determine all polynomials $P$ and $Q$ with integer coefficients such that, if we define the sequence $\left(x_{n}\right)$ by $x_{0}=2015$, $x_{2 n+1}=P\left(x_{2 n}\right)$ and $x_{2 n+2}=Q\left(x_{2 n+1}\right)$ for all $n \geqslant 0$, then every integer $m \gt 0$ divides at least one nonzero term of the sequence.