Construction of Perfect Squares and Pythagorean Triples using Continued Fractions

Abstract

Continued fractions play a major role in Number theory and solving Diophantine equations. With the help of Continued fractions and Pell’s equations, we have proved some interesting results like obtaining Pythagorean triples whose smaller sides differ by some particular integer and also we have provided methods to generate primitive Pythagorean triples satisfying a specific condition. Perfect squares are one of the most well-known class of numbers in number theory. In this paper we introduced ways to produce natural numbers that are related to perfect squares with some specified conditions.