On the quadratic residues and their distribution properties

Abstract

The main purpose of this article is to use elementary methods and properties of classical Gauss sums to determine identities for the number of residue systems of aa mod pp such that aa, a+a¯a+\bar{a}, and a−a¯a-\bar{a} are all quadratic residues, improving on results of Wang and Lv.

Keywords

• quadratic residues
• quadratic non-residues
• the classical gauss sums
• counting functions
• identity
• 11a15
• 11l40