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Computing All Integer Solutions of a General Elliptic Equation

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Algorithmic Number Theory (ANTS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1838))

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Abstract

The Elliptic Logarithm Method has been applied with great success to the problem of computing all integer solutions of equations of degree 3 and 4 defining elliptic curves. We explore the possibility of extending this method to include any equation f(u,v)=0, where f ∈ℤ[u,v] defines an irreducible curve of genus 1, independent of shape or degree of the polynomial f. We give a detailed description of the general features of our approach, putting forward along the way some claims (one of which conjectural) that are supported by the explicit examples added at the end.

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Author information

Authors and Affiliations

  1. Econometric Institute – Erasmus University, 3000 DR, Rotterdam, The Netherlands

    Roel J. Stroeker

  2. Department of Mathematics, University of Crete, GR-71409, Iraklion, Crete, Greece

    Nikolaos Tzanakis

Authors
  1. Roel J. Stroeker
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  2. Nikolaos Tzanakis
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Editor information

Editors and Affiliations

  1. Mathematisch Instituut, Universiteit Nijmegen, Postbus 9010, 6500 GL, Nijmegen, The Netherlands

    Wieb Bosma

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© 2000 Springer-Verlag Berlin Heidelberg

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Stroeker, R.J., Tzanakis, N. (2000). Computing All Integer Solutions of a General Elliptic Equation. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_37

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  • DOI: https://doi.org/10.1007/10722028_37

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67695-9

  • Online ISBN: 978-3-540-44994-2

  • eBook Packages: Springer Book Archive

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