Product-free sets with high density
Number Theory
2012-11-19 v2
Abstract
We show that there are sets of integers with asymptotic density arbitrarily close to 1 in which there is no solution to the equation ab=c, with a,b,c in the set. We also consider some natural generalizations, as well as a specific numerical example of a product-free set of integers with asymptotic density greater than 1/2.
Cite
@article{arxiv.1107.5589,
title = {Product-free sets with high density},
author = {Par Kurlberg and Jeffrey C. Lagarias and Carl Pomerance},
journal= {arXiv preprint arXiv:1107.5589},
year = {2012}
}
Comments
12 pages. Many minor edits, mainly to improve the exposition