Problem

Source: India Postal Set 5 P 3 2016

Tags: algebra, polynomial



Call a non-constant polynomial real if all its coecients are real. Let $P$ and $Q$ be polynomials with complex coefficients such that the composition $P \circ Q$ is real. Show that if the leading coefficient of $Q$ and its constant term are both real, then $P$ and $Q$ are real.