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On the equation $ Y\sp{2}=X(X\sp{2}+p)$


Authors: A. Bremner and J. W. S. Cassels
Journal: Math. Comp. 42 (1984), 257-264
MSC: Primary 11D25; Secondary 11G05, 14G05
DOI: https://doi.org/10.1090/S0025-5718-1984-0726003-4
MathSciNet review: 726003
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Abstract | References | Similar Articles | Additional Information

Abstract: Generators are found for the group of rational points on the title curve for all primes $ p \equiv 5\;\pmod 8$ less than 1,000. The rank is always 1 in accordance with conjectures of Selmer and Mordell. Some of the generators are rather large.


References [Enhancements On Off] (What's this?)

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  • [2] J. W. S. Cassels, "Diophantine equations with special reference to elliptic curves," J. London Math. Soc., v. 41, 1966, pp. 193-291. MR 0199150 (33:7299)
  • [3] L. J. Mordell, "The diophantine equation $ {x^4} + m{y^4} = {z^2}$," Quart. J. Math. (2), v. 18, 1967, pp. 1-6. MR 0210659 (35:1545)
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  • [5] E. Selmer, "A conjecture concerning rational points on cubic curves," Math. Scand., v. 2, 1954, pp. 49-54. MR 0062767 (16:14g)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1984-0726003-4
Article copyright: © Copyright 1984 American Mathematical Society

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