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arXiv · 2607.06167

An improved upper bound on the Ruzsa number

Yuchen Ding·Yu-Chen Sun·Lilu Zhao
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Abstract

Let $R_m$ be the least positive integer $r$ such that there exists a set $A\subseteq \mathbb{Z}_{m}$ with $A+A=\mathbb{Z}_m$ for which the number of ordered solutions of $n=x+y$ with $x,y\in A$ is at most $r$ for every $n\in \mathbb{Z}_m$. In this note we prove that $R_m\leqslant 128$ for every positive integer $m$, improving the previous bound $R_m\leqslant 192$.

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Yuchen Ding, Yu-Chen Sun, Lilu Zhao. 2026-07-07. An improved upper bound on the Ruzsa number. https://arxiv.org/abs/2607.06167

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