Solving Quadratic Diophantine EquationforIntegral Powers of 37

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 have solved an quadratic Diophantine equations where the right hand side are positive integral powers of 37 and provide its integer 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.