Studies of Positive Integer Solutions of the Diophantine Equation x2−ay2−bx−cy−d=0 by the Transformation Method

Abstract

Solving the Diophantine equation has fascinated mathematicians from various civilizations. In this paper, we propose the resolution of quadratic Diophantine equations with integer coefficients. Our contribution consists of generalizing certain results which have already been developed in the literature. This paper also proposes the criterion on the solvability of the quadratic Diophantine equation here studied.