Question 153
Let $P(x)$ be a polynomial of degree $n \gt 1$ with integer coefficients and let $k$ be a positive integer. Consider the polynomial
$$
Q(x) = \underbrace{P(P(\dots(P(x)\dots)))}_{k \text{ P's}}
$$
Prove that there are at most $n$ integers $t$ such that $Q(t) = t$.
$$
Q(x) = \underbrace{P(P(\dots(P(x)\dots)))}_{k \text{ P's}}
$$
Prove that there are at most $n$ integers $t$ such that $Q(t) = t$.