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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Duquesne, Sylvain 2001. Integral Points on Elliptic Curves Defined by Simplest Cubic Fields. Experimental Mathematics, Vol. 10, Issue. 1, p. 91.


    Stroeker, Roel J. and Tzanakis, Nikos 1999. On the Elliptic Logarithm Method for Elliptic Diophantine Equations: Reflections and an Improvement. Experimental Mathematics, Vol. 8, Issue. 2, p. 135.


    de Weger, Benjamin M. M. 1998. Solving Elliptic Diophantine Equations Avoiding Thue Equations and Elliptic Logarithms. Experimental Mathematics, Vol. 7, Issue. 3, p. 243.


    de Weger, Benjamin M.M. 1997. Equal Binomial Coefficients: Some Elementary Considerations. Journal of Number Theory, Vol. 63, Issue. 2, p. 373.


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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 116, Issue 3
  • November 1994, pp. 391-399

S-integral points on elliptic curves

  • N. P. Smart (a1)
  • DOI: http://dx.doi.org/10.1017/S0305004100072698
  • Published online: 24 October 2008
Abstract

In this paper I give an algorithm to find all ‘small’ S-integral points on an elliptic curve. I would like to thank N. Stephens for suggesting I consider such equations and the Wingate Foundation for supporting me whilst carrying out the research. As is usual c1, c2, …, will denote positive real constants which are effectively computable.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]M. Ayad . Points Δ-entiers sur les courbes elliptiques. J. Number Theory 38 (1991), 323337.

[4]S. Lang . Elliptic Curves: Diophantine Analysis (Springer-Verlag, 1978).

[5]A. K. Lenstra , H. W. Lenstra and L. Lovász . Factoring polynomials with rational coefficients. Math. Ann. 261 (1982), 515534.

[6]J. H. Silverman . The Arithmetic Of Elliptic Curves (Springer-Verlag, 1986).

[8]N. Tzanakis and B. M. M. De Weger . On the practical solution of the Thue equation. J. Number Theory 31 (1989), 99132.

[10]B. M. M. De Weger . Solving exponential diophantine equations using lattice basis reduction algorithms. J. Number Theory 26 (1987), 325367.

[12]D. Zagier . Large integral points on elliptic curves. Math. Comp. 48 (1987), 425436.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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