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Polynomial values of positive squares

Source: German TST 2023 AIMO 2, Problem 1

November 2, 2023
algebrapolynomial

Problem Statement

Let PP be a polynomial with integer coefficients. Assume that there exists a positive integer nn with P(n2)=2022P(n^2)=2022. Prove that there cannot be a positive rational number rr with P(r2)=2024P(r^2)=2024.
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