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Found problems: 1

2024 Middle European Mathematical Olympiad, 4
Tags: polynomial , number theory , sum of divisors , Divisibility , factorisation
Determine all polynomials $P(x)$ with integer coefficients such that $P(n)$ is divisible by $\sigma(n)$ for all positive integers $n$. (As usual, $\sigma(n)$ denotes the sum of all positive divisors of $n$.)