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Proceedings of the American Mathematical Society

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

 

 

On the number of coprime solutions of $ y^2 = x^3 + k$


Author: N. M. Stephens
Journal: Proc. Amer. Math. Soc. 48 (1975), 325-327
MSC: Primary 10B10
MathSciNet review: 0357320
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Abstract: Let $ N'(k)$ denote the number of coprime integer solutions $ x,y$ of $ {y^2} = {x^3} + k$. It is shown that $ \lim {\sup _{k \to \infty }}N'(k) \geq 8$ and that $ \lim {\sup _{k \to - \infty }}N'(k) \geq 12$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0357320-4
Article copyright: © Copyright 1975 American Mathematical Society