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arXiv · 1111.2634

The maximal density of product-free sets in Z/nZ

Par Kurlberg·Jeffrey C. Lagarias·Carl Pomerance
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Abstract

This paper studies the maximal size of product-free sets in Z/nZ. These are sets of residues for which there is no solution to ab == c (mod n) with a,b,c in the set. In a previous paper we constructed an infinite sequence of integers (n_i)_{i > 0} and product-free sets S_i in Z/n_iZ such that the density |S_i|/n_i tends to 1 as i tends to infinity, where |S_i|$ denotes the cardinality of S_i. Here we obtain matching, up to constants, upper and lower bounds on the maximal attainable density as n tends to infinity.

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Par Kurlberg, Jeffrey C. Lagarias, Carl Pomerance. 2012-01-12. The maximal density of product-free sets in Z/nZ. https://doi.org/10.1093/imrn%2Frns014

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