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Mathematics of Computation

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Prime power terms in elliptic divisibility sequences

Author: Valéry Mahé
Journal: Math. Comp. 83 (2014), 1951-1991
MSC (2010): Primary 11G05, 11A41
Published electronically: November 12, 2013
MathSciNet review: 3194137
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Abstract: We study a problem on specializations of multiples of rational points on elliptic curves analogous to the Mersenne problem. We solve this problem when descent via isogeny is possible by giving explicit bounds on the indices of prime power terms in elliptic divisibility sequences associated to points in the image of a nontrivial isogeny. We also discuss the uniformity of these bounds assuming the Hall–Lang conjecture.

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Additional Information

Valéry Mahé
Affiliation: École Polytechnique Fédérale de Lausanne, SB-IMB-CSAG, Station 8, CH-1015 Lausanne, Switzerland.

Keywords: Siegel’s Theorem, elliptic curves, isogeny, division polynomials, Thue equations, canonical height, local height
Received by editor(s): December 24, 2009
Received by editor(s) in revised form: October 15, 2011, and October 31, 2012
Published electronically: November 12, 2013
Additional Notes: This work was supported by EPSRC grant EP/E012590/1, the Université de Montpellier 2, the Université de Franche-Comté and the École Polytechnique Fédérale de Lausanne. The author thanks Professor Everest, Professor Silverman, Professor Stevens and the anonymous referee for helpful discussions and comments.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.