Question 13
Let $P(x)$ be a nonconstant integer polynomial and positive integer $n$. The sequence $a_0, a_1, \ldots$ is defined by $a_0 = n$ and $a_k = P(a_{k-1})$ for $k \ge 1$. Given that for each positive integer $b$, the sequence contains a $b$-th power of some positive integer greater than 1. Prove that $\deg P = 1$.