The maximal density of product-free sets in Z/nZ
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 (ni)i > 0 and product-free sets Si in Z/niZ such that the density |Si|/ni tends to 1 as i tends to infinity, where |Si|$ denotes the cardinality of Si. 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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