IMC 2023 · Problem 3

Day 130th IMC · Blagoevgrad, Bulgaria

Statement

Find all polynomials $P$ in two variables with real coefficients satisfying the identity

P(x, y)P(z, t) = P(xz - yt, xt + yz).

Hidden so you can work on the problem first.

Proposed by Giorgi Arabidze, Free University of Tbilisi, Georgia.