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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Prime powers in elliptic divisibility sequences


Authors: Graham Everest and Helen King
Journal: Math. Comp. 74 (2005), 2061-2071
MSC (2000): Primary 11G05, 11A41
Published electronically: March 1, 2005
MathSciNet review: 2164113
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Abstract: Certain elliptic divisibility sequences are shown to contain only finitely many prime power terms. In some cases the methods prove that only finitely many terms are divisible by a bounded number of distinct primes.


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Additional Information

Graham Everest
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: g.everest@uea.ac.uk

Helen King
Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
Email: h.king@uea.ac.uk

DOI: http://dx.doi.org/10.1090/S0025-5718-05-01737-0
PII: S 0025-5718(05)01737-0
Keywords: Elliptic curve, isogeny, prime, elliptic divisibility sequence
Received by editor(s): March 30, 2004
Received by editor(s) in revised form: April 26, 2004
Published electronically: March 1, 2005
Additional Notes: The second author was supported by an EPSRC Doctoral Training Award. Both authors thank the referee for several comments leading to improvements in the text.
Article copyright: © Copyright 2005 American Mathematical Society