Perfect powers in elliptic divisibility sequences

JOURNAL OF NUMBER THEORY

卷:132

Article

Reynolds, Jonathan

关键词: Diophantine equations;    Modular methods;    Elliptic divisibility sequences;   

DOI  :  10.1016/j.jnt.2011.09.013

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free