English

On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences

Number Theory 2021-12-21 v1

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 from y2=x(x2+b)y^2=x(x^2+b), where bb is any positive integer. We achieve this by using the modularity of elliptic curves over real quadratic number fields.

Keywords

Cite

@article{arxiv.2112.09758,
  title  = {On the Finiteness of Perfect Powers in Elliptic Divisibility Sequences},
  author = {Abdulmuhsin Alfaraj},
  journal= {arXiv preprint arXiv:2112.09758},
  year   = {2021}
}