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arXiv · 2409.03128

Ruzsa's problem on Bi-Sidon sets

János Pach·Dmitrii Zakharov
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Abstract

A subset $S$ of real numbers is called bi-Sidon if it is a Sidon set with respect to both addition and multiplication, i.e., if all pairwise sums and all pairwise products of elements of $S$ are distinct. Imre Ruzsa asked the following question: What is the maximum number $f(N)$ such that every set $S$ of $N$ real numbers contains a bi-Sidon subset of size at least $f(N)$? He proved that $f(N)\geq cN^{\frac13}$, for a constant $c>0$. In this note, we improve this bound to $N^{\frac13+\frac7{78}+o(1)}$.

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János Pach, Dmitrii Zakharov. 2024-09-13. Ruzsa's problem on Bi-Sidon sets. https://arxiv.org/abs/2409.03128

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