IMO 1976 LL USS43

Prove that if for a polynomial P(x, y) we have

IMO 1976 LL USS43

Origin: USS

Problem

Prove that if for a polynomial P(x, y) we have P(x −1, y −2x + 1) = P(x, y), then there exists a polynomial \Phi(x) with P(x, y) = \Phi(y −x2).