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Sum of f on a template is zero

Source: Ukraine TST for IMO 2018 P12

March 7, 2019
algebrafunctioncombinatorics

Problem Statement

Let nn be a positive integer and a1,a2,…,ana_1,a_2,\dots,a_n be integers. Function f:Z→Rf: \mathbb{Z} \rightarrow \mathbb{R} is such that for all integers kk and ll, l≠0l \neq 0, ∑i=1nf(k+ail)=0.\sum_{i=1}^n f(k+a_il)=0. Prove that f≡0f \equiv 0.
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