Mathematics and Computer Science, Volume 1

9A Review on the Formation of Pythagorean Triplets and Expressing an Integer as a Difference of Two Perfect Squares

Souradip Roy¹*, Tapabrata Bhattacharyya¹, Subhadip Roy¹, Souradeep Paul¹ and Arpan Adhikary^2†

¹Department of Computer Science and Engineering, Institute of Engineering & Management (IEM), Kolkata, India

²Department of Electronics and Communication Engineering, Institute of Engineering & Management (IEM), Kolkata, India

Abstract

In this paper, we have reviewed [1] the proposition for generalization of formulae that finds the primitive and nonprimitive Pythagorean triplets generated by a given integer. Besides, the procedure for finding complete expressions of the integers as a difference of two perfect squares have been formulated. Finally, the Pythagorean triplets are generated in a range from x to y, programmed with the proposed formulae, which thereby validates them.

Keywords: Pythagorean triplets, primitive and non-primitive, generalization, formularized, difference of two squares

9.1 Introduction

A Pythagorean triple is a set of positive integers (x, y, z) such that

(9.1)

From the geometrical point of view, (x, y, z) forms a set of sides, where z is the hypotenuse of a right-angled triangle. We have to find the solution to 9.1 when x, y, z are all positive integers (x, y > 2). Equation 9.1 itself ranks among the Diophantine equations. If we find one solution ...