Some Diophantine equations of the form $x^{2}-py^{2} =z$
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- by Walter Feit PDF
- Proc. Amer. Math. Soc. 129 (2001), 623-625 Request permission
Abstract:
Let $p = a^{2} + (2b)^{2}$ be a prime. It is shown that each of the two Diophantine equations $x^{2}-py^{2} =a$ or $4b$ has integral solutions.References
- Carl Friedrich Gauss, Disquisitiones arithmeticae, Yale University Press, New Haven, Conn.-London, 1966. Translated into English by Arthur A. Clarke, S. J. MR 0197380
- A.-M. Legendre, Théorie des nombres, Librairie Scientifique et Technique, A. Blanchard, Paris, 1955.
Additional Information
- Walter Feit
- Affiliation: Department of Mathematics, Yale University, Box 208283, New Haven, Connecticut 06520-8283
- Email: feit@math.yale.edu
- Received by editor(s): January 20, 2000
- Published electronically: October 2, 2000
- Communicated by: David Rohrlich
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 623-625
- MSC (2000): Primary 11D09, 11R11
- DOI: https://doi.org/10.1090/S0002-9939-00-06025-1
- MathSciNet review: 1800243