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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
DOI: https://doi.org/10.1090/S0002-9939-1973-0316377-5
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$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0316377-5
Article copyright: © Copyright 1973 American Mathematical Society