Multiplicative complements II

Anett Kocsis; Dávid Matolcsi; Csaba Sándor; György Tőtős

Multiplicative complements II

Number Theory 2023-05-08 v1

Authors: Anett Kocsis , Dávid Matolcsi , Csaba Sándor , György Tőtős

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.

Keywords

number theory perfect numbers collatz conjecture

Cite

@article{arxiv.2305.03377,
  title  = {Multiplicative complements II},
  author = {Anett Kocsis and Dávid Matolcsi and Csaba Sándor and György Tőtős},
  journal= {arXiv preprint arXiv:2305.03377},
  year   = {2023}
}

Comments

16 pages

Related papers

View all related →