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International Algorithmic Number Theory Symposium

ANTS 2002: Algorithmic Number Theory pp 95–107Cite as

A Higher-Rank Mersenne Problem

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2369))

Abstract

The classical Mersenne problem has been a stimulating challenge to number theorists and computer scientists for many years. After briefly reviewing some of the natural settings in which this problem appears as a special case, we introduce an analogue of the Mersenne problem in higher rank, in both a classical and an elliptic setting. Numerical evidence is presented for both cases, and some of the difficulties involved in developing even a heuristic understanding of the problem are discussed.

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Author information

Authors and Affiliations

  1. School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, UK

    Graham Everest, Peter Rogers & Thomas Ward

Authors
  1. Graham Everest
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  2. Peter Rogers
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  3. Thomas Ward
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, F07, University of Sydney, Sydney, NSW, 2006, Australia

    Claus Fieker  & David R. Kohel  & 

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Everest, G., Rogers, P., Ward, T. (2002). A Higher-Rank Mersenne Problem. In: Fieker, C., Kohel, D.R. (eds) Algorithmic Number Theory. ANTS 2002. Lecture Notes in Computer Science, vol 2369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45455-1_8

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  • DOI: https://doi.org/10.1007/3-540-45455-1_8

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43863-2

  • Online ISBN: 978-3-540-45455-7

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