标题： 在$O(n\log\log\log n)$时间内找到Erdős-Ginzburg-Ziv定理的解 显示英文标题

标题： Finding a solution to the Erdős-Ginzburg-Ziv theorem in $O(n\log\log\log n)$ time

摘要： 埃拉托色尼-金斯伯格-齐夫定理指出，对于任何长度为$2n-1$的整数序列，都存在一个长度为$n$的子序列，其和能被$n$整除。 在本文中，我们提供了一个简单、实用的$O(n\log\log n)$算法和一个理论上的$O(n\log\log\log n)$算法，两者都优于之前已知的最佳$O(n\log n)$方法。 这表明一种特定的布尔卷积变体可以在比基于FFT的方法通常预期的$O(n\log n)$时间内实现。 显示英文摘要

摘要： The Erd\H{o}s-Ginzburg-Ziv theorem states that for any sequence of $2n-1$ integers, there exists a subsequence of $n$ elements whose sum is divisible by $n$. In this article, we provide a simple, practical $O(n\log\log n)$ algorithm and a theoretical $O(n\log\log\log n)$ algorithm, both of which improve upon the best previously known $O(n\log n)$ approach. This shows that a specific variant of boolean convolution can be implemented in time faster than the usual $O(n\log n)$ expected from FFT-based methods.