Solution of planar Diophantine equations
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- by James C. Owings PDF
- Proc. Amer. Math. Soc. 72 (1978), 1-5 Request permission
Abstract:
We continue our investigation, begun in [2], of the “planes” associated with the Diophantine equation \[ {x^2} + {y^2} + {z^2} \pm yz \pm xz \pm xy + gx + hy + kz + m = 0.\] 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
- W. H. Mills, A method for solving certain Diophantine equations, Proc. Amer. Math. Soc. 5 (1954), 473–475. MR 62757, DOI 10.1090/S0002-9939-1954-0062757-3
- James C. Owings Jr., An elementary approach to Diophantine equations of the second degree, Duke Math. J. 37 (1970), 261–273. MR 260669
Additional Information
- © Copyright 1978 American Mathematical Society
- 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