On Solving Generalized Quadratic Diophantine Equation Dx^2+y^2=(D+λ^2 )^n

Abstract

Diophantine Equations named after ancient Greek mathematician Diophantus, plays a vital role not only in number theory but also in several branches of mathematics. In this paper, we have solved specific class of quadratic Diophantine equation and obtained its complete solutions. As verification, we have solved some of its particular cases.