Perfect powers in elliptic divisibility sequences

7Citations
Citations of this article
8Readers
Mendeley users who have this article in their library.

Abstract

It is shown that there are finitely many perfect powers in an elliptic divisibility sequence whose first term is divisible by 2 or 3. For Mordell curves the same conclusion is shown to hold if the first term is greater than 1. Examples of Mordell curves and families of congruent number curves are given with corresponding elliptic divisibility sequences having no perfect power terms. The proofs combine primitive divisor results with modular methods for Diophantine equations. © 2012 Elsevier Inc.

Cite

CITATION STYLE

APA

Reynolds, J. (2012). Perfect powers in elliptic divisibility sequences. Journal of Number Theory, 132(5), 998–1015. https://doi.org/10.1016/j.jnt.2011.09.013

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free