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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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