IMC 2018 · Problem 9

Day 225th IMC · Blagoevgrad, Bulgaria

Statement

Determine all pairs $P(x)$ , $Q(x)$ of complex polynomials with leading coefficient $1$ such that $P(x)$ divides $Q(x)^2 + 1$ and $Q(x)$ divides $P(x)^2 + 1$ .

Official solution

Hidden so you can work on the problem first.

Proposed by Rodrigo Angelo, Princeton University and Matheus Secco, PUC, Rio de Janeiro.