A note on Mordell’s equation $y^{2}=x^{3}+k$
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 $(x,y) = 1$.
- 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 https://doi.org/10.1112/jlms/s1-41.1.523 J. P. Serre, $P$-torsion des courbes elliptiques, Seminaire Bourbaki no. 380 (1970).
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Article copyright:
© Copyright 1973
American Mathematical Society
