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2009 divides f(c) for some c

Source: Indonesia IMO 2010 TST, Stage 1, Test 3, Problem 1

November 12, 2009
algebrapolynomialnumber theory proposednumber theory

Problem Statement

Let f f be a polynomial with integer coefficients. Assume that there exists integers a a and b b such that f(a)\equal{}41 and f(b)\equal{}49. Prove that there exists an integer c c such that 2009 2009 divides f(c) f(c). Nanang Susyanto, Jogjakarta
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