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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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A note on Mordell’s equation $y^{2}=x^{3}+k$
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by S. P. Mohanty PDF
Proc. Amer. Math. Soc. 39 (1973), 645-646 Request permission

Abstract:

In this note we prove that $\lim {\sup _{k \to \infty }}N’(k) \geqq 6$, where $N’(k)$ is the number of integral solutions of ${y^2} = {x^3} + k$ with $(x,y) = 1$.
References
  • L. J. Mordell, On some Diophantine equations $y^2=x^3+k$ with no rational solutions, Arch. Math. Naturvid. 49 (1947), no. 6, 143–150. MR 22857
  • L. J. Mordell, The infinity of rational solutions of $y^{2}=x^{3}+k$, J. London Math. Soc. 41 (1966), 523–525. MR 197394, DOI 10.1112/jlms/s1-41.1.523
    • J. P. Serre, $P$-torsion des courbes elliptiques, Seminaire Bourbaki no. 380 (1970).
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Additional Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 39 (1973), 645-646
  • MSC: Primary 10B10; Secondary 14G25, 14H25
  • DOI: https://doi.org/10.1090/S0002-9939-1973-0316377-5
  • MathSciNet review: 0316377