On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

Abdulmuhsin Alfaraj

doi:10.5802/jtnb.1244

On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

Abdulmuhsin Alfaraj

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (SciVal)

Abstract

We prove that there are finitely many perfect powers in elliptic divisibility sequences generated by a non-integral point on elliptic curves of the form y² = x(x² + b), where b is any positive integer. We achieve this by using the modularity of elliptic curves over real quadratic number fields.

Original language	English
Pages (from-to)	247-258
Number of pages	12
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	35
Issue number	1
Early online date	4 May 2023
DOIs	https://doi.org/10.5802/jtnb.1244
Publication status	Published - 31 Dec 2023

ASJC Scopus subject areas

Algebra and Number Theory

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10.5802/jtnb.1244Licence: CC BY-ND

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abstract = "We prove that there are finitely many perfect powers in elliptic divisibility sequences generated by a non-integral point on elliptic curves of the form y2 = x(x2 + b), where b is any positive integer. We achieve this by using the modularity of elliptic curves over real quadratic number fields.",

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On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

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