On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)247-258
Number of pages12
JournalJournal de Theorie des Nombres de Bordeaux
Volume35
Issue number1
Early online date4 May 2023
DOIs
Publication statusPublished - 31 Dec 2023

ASJC Scopus subject areas

  • Algebra and Number Theory

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