## Prime power terms in elliptic divisibility sequences

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- by Valéry Mahé;
- Math. Comp.
**83**(2014), 1951-1991 - DOI: https://doi.org/10.1090/S0025-5718-2013-02790-1
- Published electronically: November 12, 2013
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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.## References

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## Bibliographic Information

**Valéry Mahé**- Affiliation: École Polytechnique Fédérale de Lausanne, SB-IMB-CSAG, Station 8, CH-1015 Lausanne, Switzerland.
- Email: valery.mahe@epfl.ch
- 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.
- © Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp.
**83**(2014), 1951-1991 - MSC (2010): Primary 11G05, 11A41
- DOI: https://doi.org/10.1090/S0025-5718-2013-02790-1
- MathSciNet review: 3194137