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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

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