Multiplicative complements II
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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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | 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. |
|---|---|
| DOI: | 10.48550/arxiv.2305.03377 |