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Maximum Absolute Values of Coefficients of Polynomials

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

April 5, 2023
algebrapolynomialabsolute value

Problem Statement

Let P(x),Q(x),R(x)P(x), Q(x), R(x) be polynomials with integer coefficients, such that P(x)=Q(x)R(x)P(x) = Q(x)R(x). Let's denote by aa and bb the largest absolute values of coefficients of P,QP, Q correspondingly. Does b≤2023ab \le 2023a always hold?
Proposed by Dmytro Petrovsky
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