Question 18
Let $P(x)$ and $Q(x)$ be non-constant real polynomials such that for every positive integer $m$, there exists a positive integer $n$ with $P(m) = Q(n)$.
(1) Prove that if $\deg(Q)$ divides $\deg(P)$, then there exists a real polynomial $h(x)$ such that $P(x) = Q(h(x))$.
(2) Prove that $\deg(Q)$ divides $\deg(P)$.
(1) Prove that if $\deg(Q)$ divides $\deg(P)$, then there exists a real polynomial $h(x)$ such that $P(x) = Q(h(x))$.
(2) Prove that $\deg(Q)$ divides $\deg(P)$.