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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A note on Mordell's equation $ y\sp{2}=x\sp{3}+k$


Author: S. P. Mohanty
Journal: Proc. Amer. Math. Soc. 39 (1973), 645-646
MSC: Primary 10B10; Secondary 14G25, 14H25
MathSciNet review: 0316377
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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 [Enhancements On Off] (What's this?)

  • [1] L. J. Mordell, On some Diophantine equations 𝑦²=𝑥³+𝑘 with no rational solutions, Arch. Math. Naturvid. 49 (1947), no. 6, 143–150. MR 0022857 (9,270b)
  • [2] L. J. Mordell, The infinity of rational solutions of 𝑦²=𝑥³+𝑘, J. London Math. Soc. 41 (1966), 523–525. MR 0197394 (33 #5559)
  • [3] J. P. Serre, $ P$-torsion des courbes elliptiques, Seminaire Bourbaki no. 380 (1970).

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1973-0316377-5
PII: S 0002-9939(1973)0316377-5
Article copyright: © Copyright 1973 American Mathematical Society