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Source: 2024 Vietnam National Olympiad - Problem 2

January 5, 2024
algebrapolynomial

Problem Statement

Find all polynomials P(x),Q(x)P(x), Q(x) with real coefficients such that for all real numbers aa, P(a)P(a) is a root of the equation x2023+Q(a)x2+(a2024+a)x+a3+2025a=0.x^{2023}+Q(a)x^2+(a^{2024}+a)x+a^3+2025a=0.
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