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 $b \le 2023a$ always hold? Proposed by Dmytro Petrovsky