Finding All Natural Solutions of the Hyperbola Equation by a new Form

Abstract

Abstract: In this paper a new form has been found that gives all natural solutions to the hyperbola equation x^2-dy^2=c^2 where cϵN, d is a positive square free number. It has been depended of Pell's equation〖 x〗^2-dy^2=1 and a continued fraction method for a real number √d .