Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
MathSciNet review: 0498366
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • [1] W. H. Mills, A method for solving certain Diophantine equations, Proc. Amer. Math. Soc. 5 (1954), 473-475. MR 0062757 (16:13e)
  • [2] J. C. Owings, Jr., An elementary approach to Diophantine equations of the second degree, Duke Math. J. 37 (1970), 261-273. MR 0260669 (41:5293)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 10B05

Retrieve articles in all journals with MSC: 10B05

Additional Information

Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society