On Multiplicative Sidon Sets

Details On Multiplicative Sidon Sets On Multiplicative Sidon Sets

2011-07-06

arxiv.org/abs/1107.1073v1

Mathematics

Number Theory

Scientific paper

Fix integers $b>a\geq1$ with $g:=\gcd(a,b)$. A set $S\subseteq\mathbb{N}$ is
\emph{$\{a,b\}$-multiplicative} if $ax\neq by$ for all $x,y\in S$. For all $n$,
we determine an $\{a,b\}$-multiplicative set with maximum cardinality in $[n]$,
and conclude that the maximum density of an $\{a,b\}$-multiplicative set is
$\frac{b}{b+g}$.

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