Problem

Source: Ukrainian Mathematical Olympiad 2023. Day 2, Problem 10.6

Tags: algebra, polynomial, absolute value



Let P(x),Q(x),R(x) be polynomials with integer coefficients, such that P(x)=Q(x)R(x). Let's denote by a and b the largest absolute values of coefficients of P,Q correspondingly. Does b2023a always hold? Proposed by Dmytro Petrovsky