Primes in elliptic divisibility sequences

Einsiedler, M.; Everest, G.; Ward, T.

Abstract

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

Citation

Einsiedler, M., Everest, G., & Ward, T. (2001). Primes in elliptic divisibility sequences. LMS journal of computation and mathematics, 4, 1-13. https://doi.org/10.1112/s1461157000000772

• Journal Article Type: Article
• Publication Date: Jan 1, 2001
• Deposit Date: Oct 12, 2012
• Journal: LMS Journal of Computation and Mathematics
• Electronic ISSN: 1461-1570
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 4
• Pages: 1-13
• DOI: https://doi.org/10.1112/s1461157000000772
• Public URL: https://durham-repository.worktribe.com/output/1502489
• Publisher URL: http://old.lms.ac.uk/jcm//4/lms2000-027/sub/lms2000-027.pdf?q=jcm/4/lms2000-027/sub/lms2000-027.pdf