IMO 1969 LL POL54

Given a polynomial f(x) with integer coefficients whose value

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IMO 1969 LL POL54

Origin: POL

Problem

Given a polynomial f(x) with integer coefficients whose value is divisible by 3 for three integers k, k + 1, and k + 2, prove that f(m) is divisible by 3 for all integers m.