Question 129
Let $P(x)$ be a non-constant polynomial with real coefficients such that $P(0) = 0$. For all positive real numbers $M$, prove that there is a positive integer $d$ such that for any monic polynomial $Q(x)$ of degree greater than or equal to $d$, total number of integers $k$ where
$$
|P(Q(k))| \leq M,
$$
is at most $\deg Q(x)$.
$$
|P(Q(k))| \leq M,
$$
is at most $\deg Q(x)$.