On sets of integers which are both sum-free and product-free

Details On sets of integers which are both sum-free and product-free On sets of integers which are both sum-free and product-free

2012-01-05

arxiv.org/abs/1201.1317v1

Mathematics

Number Theory

8 pages

Scientific paper

We consider sets of positive integers containing no sum of two elements in
the set and also no product of two elements. We show that the upper density of
such a set is strictly smaller than 1/2 and that this is best possible.
Further, we also find the maximal order for the density of such sets that are
also periodic modulo some positive integer.

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