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Problem 1-Polynomial

Source: Danube Mathematical Competition 2017, Romania

October 28, 2017
algebrapolynomial

Problem Statement

Find all polynomials P(x)P(x) with integer coefficients such that a2+b2−c2a^2+b^2-c^2 divides P(a)+P(b)−P(c)P(a)+P(b)-P(c), for all integers a,b,ca,b,c.
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