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

الأصل · EN

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.