How to solve a quadratic equation in integers
Fritz J. Grunewald, Dan Segal · Mathematical Proceedings of the Cambridge Philosophical Society · 1981
In answer to a question posed by J. L Britton in (2), we sketch in this note an effective procedure to decide whether an arbitrary quadratic equation with rational coefficients, has a solution in integers. A similar procedure will in fact decide whether such an equation over a (suitably specified) algebraic number field k has a solution in any (suitably specified) order in k; but we shall not burden the exposition by giving chapter and verse for this claim.