Counting the number of Pythagorean triples in finite fields

Abstract

It is well-known that the set of quadratic residues modulo prime p forms a multiplicative group. Apart from special cases there is no result concerning the sum of two quadratic residues. Here the authors consider these sums. Formulae for the total number of quadratic residues which can be stated as the sum of two quadratic residues are obtained. These formulae have been used to obtain the integer triples satisfying the Pythagorean equation in prime modes.