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NT with iteration of polynomial and perfect squares

Source: Serbia 2024 MO Problem 6

April 4, 2024
number theory

Problem Statement

Find all non-constant polynomials P(x)P(x) with integer coefficients and positive leading coefficient, such that P2mn(m2)+n2P^{2mn}(m^2)+n^2 is a perfect square for all positive integers m,nm, n.
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