Let $ f$ be a polynomial with integer coefficients. Assume that there exists integers $ a$ and $ b$ such that $ f(a)=41$ and $ f(b)=49$. Prove that there exists an integer $ c$ such that $ 2009$ divides $ f(c)$. Nanang Susyanto, Jogjakarta
Problem
Source: Indonesia IMO 2010 TST, Stage 1, Test 3, Problem 1
Tags: algebra, polynomial, number theory proposed, number theory