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Divisibility with iteration of a polynomial

Source: IMSC 2023 Mock IMO P6

July 13, 2023
algebrapolynomial

Problem Statement

Find all polynomials P(x)P(x) with integer coefficients, such that for all positive integers m,nm, n, m+n∣P(m)(n)−P(n)(m).m+n \mid P^{(m)}(n)-P^{(n)}(m).
Proposed by Navid Safaei, Iran
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