---
_id: '12309'
abstract:
- lang: eng
  text: Take a rational elliptic curve defined by the equation y2=x3+ax in minimal
    form and consider the sequence Bn of the denominators of the abscissas of the
    iterate of a non-torsion point. We show that B5m has a primitive divisor for every
    m. Then, we show how to generalize this method to the terms of the form Bmp with
    p a prime congruent to 1 modulo 4.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Matteo
  full_name: Verzobio, Matteo
  id: 7aa8f170-131e-11ed-88e1-a9efd01027cb
  last_name: Verzobio
  orcid: 0000-0002-0854-0306
citation:
  ama: Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic
    curves with j=1728. <i>Acta Arithmetica</i>. 2021;198(2):129-168. doi:<a href="https://doi.org/10.4064/aa191016-30-7">10.4064/aa191016-30-7</a>
  apa: Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences
    for elliptic curves with j=1728. <i>Acta Arithmetica</i>. Institute of Mathematics,
    Polish Academy of Sciences. <a href="https://doi.org/10.4064/aa191016-30-7">https://doi.org/10.4064/aa191016-30-7</a>
  chicago: Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences
    for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>. Institute of Mathematics,
    Polish Academy of Sciences, 2021. <a href="https://doi.org/10.4064/aa191016-30-7">https://doi.org/10.4064/aa191016-30-7</a>.
  ieee: M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic
    curves with j=1728,” <i>Acta Arithmetica</i>, vol. 198, no. 2. Institute of Mathematics,
    Polish Academy of Sciences, pp. 129–168, 2021.
  ista: Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for
    elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168.
  mla: Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for
    Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>, vol. 198, no. 2, Institute
    of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:<a href="https://doi.org/10.4064/aa191016-30-7">10.4064/aa191016-30-7</a>.
  short: M. Verzobio, Acta Arithmetica 198 (2021) 129–168.
date_created: 2023-01-16T11:44:54Z
date_published: 2021-01-04T00:00:00Z
date_updated: 2023-05-08T11:58:14Z
day: '04'
doi: 10.4064/aa191016-30-7
extern: '1'
external_id:
  arxiv:
  - '2001.09634'
intvolume: '       198'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2001.09634
month: '01'
oa: 1
oa_version: Preprint
page: 129-168
publication: Acta Arithmetica
publication_identifier:
  issn:
  - 0065-1036
  - 1730-6264
publication_status: published
publisher: Institute of Mathematics, Polish Academy of Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primitive divisors of elliptic divisibility sequences for elliptic curves with
  j=1728
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 198
year: '2021'
...