On Solving Euler’s Quadratic Diophantine Equation

Abstract

Diophantine Equations plays a vital role not only in number theory but also in several branches of science. Leonhard Euler was considered to be the most prolific mathematician of all times. In this paper, we will solve one of the problems posed by Euler which turns out to be a Quadratic Diophantine Equation. The method adopted to solve the problem is quite novel and can be generalized for solving similar equations.