On Solving a Quadratic Diophantine Equation Involving Odd Powers of 17

Abstract

Diophantine Equations named after ancient Greek mathematician Diophantus, plays a vital role not only in number theory but also in several branches of science. In this paper, we will solve one of the quadratic Diophantine equations where the right hand side are odd positive integral powers of 17 and provide its complete solutions. The method adopted to solve the given equation is using the concept of polar form of a particular complex number. This concept can be generalized for solving similar equations.