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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Solution of planar Diophantine equations


Author: James C. Owings
Journal: Proc. Amer. Math. Soc. 72 (1978), 1-5
MSC: Primary 10B05
DOI: https://doi.org/10.1090/S0002-9939-1978-0498366-8
MathSciNet review: 0498366
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Abstract: We continue our investigation, begun in [2], of the ``planes'' associated with the Diophantine equation

$\displaystyle {x^2} + {y^2} + {z^2} \pm yz \pm xz \pm xy + gx + hy + kz + m = 0.$

In particular, we show that the number of planes is finite, thus providing a new way of finding all integral solutions of this equation. Hopefully, our methods will extend to a treatment of the general quadratic equation in three variables.

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DOI: https://doi.org/10.1090/S0002-9939-1978-0498366-8
Article copyright: © Copyright 1978 American Mathematical Society