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Polynomial divisible by sum of divisors

Source: MEMO 2024 I4

August 26, 2024
polynomialnumber theorysum of divisorsDivisibilityfactorisation

Problem Statement

Determine all polynomials P(x)P(x) with integer coefficients such that P(n)P(n) is divisible by σ(n)\sigma(n) for all positive integers nn. (As usual, σ(n)\sigma(n) denotes the sum of all positive divisors of nn.)
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