Question 17
Find all polynomials $P, Q \in \mathbb{Z}[x]$ such that every positive integer is a divisor of a certain nonzero term of the sequence $\left(x_{n}\right)_{n=0}^{\infty}$ given by the conditions:
$$
x_{0}=2016,\quad x_{2 n+1}=P\left(x_{2 n}\right),\quad x_{2 n+2}=Q\left(x_{2 n+1}\right) \text{ for all } n \geq 0.
$$
$$
x_{0}=2016,\quad x_{2 n+1}=P\left(x_{2 n}\right),\quad x_{2 n+2}=Q\left(x_{2 n+1}\right) \text{ for all } n \geq 0.
$$