IMO 1992 LL THA71

Origin: THA

Problem

Let P1(x, y) and P2(x, y) be two relatively prime polynomials with complex coefficients. Let Q(x, y) and R(x, y) be polynomials with complex coefficients and each of degree not exceeding d. Prove that there exist two integers A1, A2 not simultaneously zero with |Ai| \leqd + 1 (i = 1, 2) and such that the polynomial A1P1(x, y) + A2P2(x, y) is coprime to Q(x, y) and R(x, y).