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How to solve a quadratic equation in integers

Published online by Cambridge University Press:  24 October 2008

Fritz J. Grunewald  and
Daniel Segal
Fritz J. Grunewald
Affiliation:
Sonderforschungsbereich Theoretische Mathematik, Bonn, and U.M.I.S.T., Manchester
Daniel Segal
Affiliation:
Sonderforschungsbereich Theoretische Mathematik, Bonn, and U.M.I.S.T., Manchester
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Extract

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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 1 - 5
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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