Simple deterministic O(n log n) algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem

Abstract

Erd\H{o}s-Ginzburg-Ziv theorem is a famous theorem in additive number theory, which states any sequence of $2n-1$ integers contains a subsequence of $n$ elements, with their sum being a multiple of $n$. In this article, we provide an algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem in $\mathcal{O}(n \log n)$ time. This is the first known deterministic $\mathcal{O}(n \log n)$ time algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem.