On the Generation of Pythagorean Triples and Representation of Integers as a Difference of Two Squares

TL;DR

This paper presents formulas for generating Pythagorean triples and representing integers as differences of two squares, advancing understanding of number representations and their generation methods.

Contribution

It introduces new formulas for counting primitive and nonprimitive triples generated by a number and for representing integers as differences of two squares.

Findings

Formulas for counting Pythagorean triples generated by a given number

Formulas for representing integers as a difference of two squares

Complete characterization of such representations

Abstract

The general formulas for finding the quantity of all primitive and nonprimitive triples generated by the given number x have been proposed. Also the formulas for finding the complete quantity of the representations of the integers as a difference of two squares have been obtained.