Journal
JOURNAL OF NUMBER THEORY
Volume 128, Issue 4, Pages 918-925Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jnt.2007.07.001
Keywords
quadratic residue; quadratic nonresidue; legendre symbol; residue representative; residue partition
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If S is a nonempty finite set of positive integers, we find a criterion both necessary and sufficient for S to satisfy the following condition: if q is a fixed nonnegative integer, then there exists infinitely many primes p such that S contains exactly q quadratic residues of p. This result simultaneously generalizes two previous results of the author, and the criterion used is expressed by means of a purely combinatorial condition on the prime factors of the elements of S of odd multiplicity. (c) 2007 Elsevier Inc. All rights reserved.
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