Question 37
Let $P(x), Q(x) \in \mathbb{R}[x]$ be polynomials with real coefficients such that
$$
P(P(x)) = (Q(x))^2
$$
holds for all real numbers $x$.
Does there necessarily exist a polynomial $R(x) \in \mathbb{R}[x]$ with real coefficients such that $P(x) = (R(x))^2$ holds for all real numbers $x$?
$$
P(P(x)) = (Q(x))^2
$$
holds for all real numbers $x$.
Does there necessarily exist a polynomial $R(x) \in \mathbb{R}[x]$ with real coefficients such that $P(x) = (R(x))^2$ holds for all real numbers $x$?