Quadratic residues and the combinatorics of sign multiplication
Given a nonempty finite set \(S\) of positive integers and an integer \(q \geq 0\), the author gives an if and only if condition for the existence of infinitely many prime numbers \(p\) such that \(S\) contains exactly \(q\) quadratic residues modulo \(p\). The criterion and the proofs are combinatorial in nature and involve the prime factors, of odd multiplicity, of the elements of \(S\) and generalize previous results of the author [J. Number Theory 123, No. 1, 120--132 (2007; Zbl 1111.11003)].
scientific article; zbMATH DE number 5378836