MathDB
Prove that the function is null

Source: IMC 2007, Day 1, Problem 5

August 6, 2007
functionmodular arithmeticalgebrapolynomialinductionIMCcollege contests

Problem Statement

Let n n be a positive integer and a1,…,an a_{1}, \ldots, a_{n} be arbitrary integers. Suppose that a function f:Z→R f: \mathbb{Z}\to \mathbb{R} satisfies ∑i=1nf(k+ail)=0 \sum_{i=1}^{n}f(k+a_{i}l) = 0 whenever k k and l l are integers and l≠0 l \ne 0. Prove that f=0 f = 0.
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