---
_id: '12308'
abstract:
- lang: eng
  text: Let P and Q be two points on an elliptic curve defined over a number field
    K. For α∈End(E), define Bα to be the OK-integral ideal generated by the denominator
    of x(α(P)+Q). Let O be a subring of End(E), that is a Dedekind domain. We will
    study the sequence {Bα}α∈O. We will show that, for all but finitely many α∈O,
    the ideal Bα has a primitive divisor when P is a non-torsion point and there exist
    two endomorphisms g≠0 and f so that f(P)=g(Q). This is a generalization of previous
    results on elliptic divisibility sequences.
article_number: '37'
article_processing_charge: No
article_type: original
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 sequences associated to elliptic curves with
    complex multiplication. <i>Research in Number Theory</i>. 2021;7(2). doi:<a href="https://doi.org/10.1007/s40993-021-00267-9">10.1007/s40993-021-00267-9</a>
  apa: Verzobio, M. (2021). Primitive divisors of sequences associated to elliptic
    curves with complex multiplication. <i>Research in Number Theory</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s40993-021-00267-9">https://doi.org/10.1007/s40993-021-00267-9</a>
  chicago: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic
    Curves with Complex Multiplication.” <i>Research in Number Theory</i>. Springer
    Nature, 2021. <a href="https://doi.org/10.1007/s40993-021-00267-9">https://doi.org/10.1007/s40993-021-00267-9</a>.
  ieee: M. Verzobio, “Primitive divisors of sequences associated to elliptic curves
    with complex multiplication,” <i>Research in Number Theory</i>, vol. 7, no. 2.
    Springer Nature, 2021.
  ista: Verzobio M. 2021. Primitive divisors of sequences associated to elliptic curves
    with complex multiplication. Research in Number Theory. 7(2), 37.
  mla: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves
    with Complex Multiplication.” <i>Research in Number Theory</i>, vol. 7, no. 2,
    37, Springer Nature, 2021, doi:<a href="https://doi.org/10.1007/s40993-021-00267-9">10.1007/s40993-021-00267-9</a>.
  short: M. Verzobio, Research in Number Theory 7 (2021).
date_created: 2023-01-16T11:44:39Z
date_published: 2021-05-20T00:00:00Z
date_updated: 2023-05-08T12:00:17Z
day: '20'
doi: 10.1007/s40993-021-00267-9
extern: '1'
intvolume: '         7'
issue: '2'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.1007/s40993-021-00267-9
month: '05'
oa: 1
oa_version: Published Version
publication: Research in Number Theory
publication_identifier:
  issn:
  - 2522-0160
  - 2363-9555
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primitive divisors of sequences associated to elliptic curves with complex
  multiplication
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2021'
...