Product-free sets with high density

Details Product-free sets with high density Product-free sets with high density

2011-07-27

arxiv.org/abs/1107.5589v2

Mathematics

Number Theory

12 pages. Many minor edits, mainly to improve the exposition

Scientific paper

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.

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