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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The solvability of the equation $ax^{2}+by^{2}=c$ in quadratic fields
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by Neal Plotkin PDF
Proc. Amer. Math. Soc. 34 (1972), 337-339 Request permission

Abstract:

In a recent paper, L. J. Mordell gave necessary and sufficient conditions for the equation $a{x^2} + b{y^2} = c$ to have algebraic integer solutions in the quadratic field $Q(\surd ( - n))$. In this paper we drop the requirement that the solutions be algebraic integers. In particular, we prove that $a{x^2} + b{y^2} = c$ has solutions in $Q(\surd ( - n))$ if and only if the quadratic form $ab{t^2} - bc{u^2} - ac{v^2} - n{w^2}$ represents 0 over Q.
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 337-339
  • MSC: Primary 12A25
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0297736-5
  • MathSciNet review: 0297736