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Primes in Elliptic Divisibility Sequences

Published online by Cambridge University Press:  01 February 2010

Manfred Einsiedler ,
Graham Everest  and
Thomas Ward
Manfred Einsiedler
Affiliation:
Mathematical Institute, University of Vienna, Strudlhofgasse 4, A-1090 Wien, Austria, Manfred.Einsiedler@univie.ac.at
Graham Everest
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, G.Everest@uea.ac.uk
Thomas Ward
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, T.Ward@uea.ac.uk

Abstract

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Morgan Ward pursued the study of elliptic divisibility sequences, originally initiated by Lucas, and Chudnovsky and Chudnovsky subsequently suggested looking at elliptic divisibility sequences for prime appearance. The problem of prime appearance in these sequences is examined here, from both a theoretical and a practical viewpoint. We show calculations, together with a heuristic argument, to suggest that these sequences contain only finitely many primes.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 4 , 2001 , pp. 1 - 13
Copyright
Copyright © London Mathematical Society 2001

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