Finding all natural solutions of the hyperbola equation by a new form

الملخص EN

In this paper a new form has been found that gives all natural solutions to the hyperbola equation ?2 − ??2 = ?2 where ??? , ? is a positive square free number.

It has been depended of Pell's equation ?2 − ??2 = 1 and a continued fraction method for a real number √? .