Multiplicative complements II

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 $\underset{x\to \infty }{\lim }\frac{A(x)B(x)}{x}=\infty$. We also prove many other results about sets like this.

16 pages