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Easy oly poly divisibility

Source: Baltic Way 2021, Problem 19

November 15, 2021
number theorynumber theory proposedPolynomials

Problem Statement

Find all polynomials pp with integer coefficients such that the number p(a)−p(b)p(a) - p(b) is divisible by a+ba + b for all integers a,ba, b, provided that a+b≠0a + b \neq 0.
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