Partition of quadratic residues and non-residues in $$\mathbb {Z}_p^*$$ for an odd prime p

Abstract

Let p be an odd prime. In this article, we investigate the number of ways in which a quadratic residue and a non-residue modulo p can be expressed as sum of two quadratic residues sum of two quadratic non-residues, and sum of a quadratic residue and non-residue in an elementary way using Gauss sums.