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Quadratic polynomial, coefficients divisible by 5

Source: IMC 2007, Day 1, Problem 1

August 6, 2007
quadraticsalgebrapolynomialmodular arithmeticIMCcollege contests

Problem Statement

Let f f be a polynomial of degree 2 with integer coefficients. Suppose that f(k) f(k) is divisible by 5 for every integer k k. Prove that all coefficients of f f are divisible by 5.
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