THE MAXIMAL DENSITY OF PRODUCT-FREE SETS IN Z/nZ
نویسندگان
چکیده
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≥1 and product-free sets Si in Z/niZ such that the density |Si|/ni → 1 as i → ∞, 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→∞.
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تاریخ انتشار 2012