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arXiv · 2305.03377

Multiplicative complements II

Anett Kocsis·Dávid Matolcsi·Csaba Sándor·György Tőtős
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Abstract

In this paper we prove that if $A$ and $B$ are infinite subsets of positive integers such that every positive integer $n$ can be written as $n=ab$, $a\in A$, $b\in B$, then $\displaystyle \lim_{x\to \infty}\frac{A(x)B(x)}{x}=\infty $. We also prove many other results about sets like this.

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Anett Kocsis, Dávid Matolcsi, Csaba Sándor, György Tőtős. 2023-05-05. Multiplicative complements II. https://arxiv.org/abs/2305.03377

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