Dense sumsets of Sidon sequences

Sándor Z. Kiss; Csaba Sándor

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arXiv · 2103.10349

Dense sumsets of Sidon sequences

Sándor Z. Kiss·Csaba Sándor

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Abstract

Let $k \ge 2$ be an integer. We say a set $A$ of positive integers is an asymptotic basis of order $k$ if every large enough positive integer can be represented as the sum of $k$ terms from $A$. A set of positive integers $A$ is called Sidon set if all the two terms sums formed by the elements of $A$ are different. Many years ago P. Erd\H{o}s, A. S\'ark\"ozy and V. T. S\'os asked whether there exists a Sidon set which is asymptotic basis of order $3$. In this paper we prove the existence of a Sidon set $A$ with positive lower density of the three fold sumset $A + A + A$ by using probabilistic methods.

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Sándor Z. Kiss, Csaba Sándor. 2021-03-18. Dense sumsets of Sidon sequences. https://arxiv.org/abs/2103.10349

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