Article ID Journal Published Year Pages File Type
4594034 Journal of Number Theory 2013 33 Pages PDF
Abstract

Let SS be an infinite set of nonempty, finite subsets of the positive integers. If p   is an odd prime, let c(p)c(p) denote the cardinality of the set {S∈S:S⊆{1,…,p−1} and S is a set of quadratic residues (respectively, non-residues) of p}{S∈S:S⊆{1,…,p−1} and S is a set of quadratic residues (respectively, non-residues) of p}. When SS is constructed in various ways from the set of all arithmetic progressions of positive integers, we determine the sharp asymptotic behavior of c(p)c(p) as p→+∞p→+∞. Generalizations and variations of this are also established, and some problems connected with these results that are worthy of further study are discussed.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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