---
_id: '12313'
abstract:
- lang: eng
  text: Let P be a nontorsion point on an elliptic curve defined over a number field
    K and consider the sequence {Bn}n∈N of the denominators of x(nP). We prove that
    every term of the sequence of the Bn has a primitive divisor for n greater than
    an effectively computable constant that we will explicitly compute. This constant
    will depend only on the model defining the curve.
acknowledgement: "This paper is part of the author’s PhD thesis at Università of Pisa.
  Moreover, this\r\nproject has received funding from the European Union’s Horizon
  2020 research\r\nand innovation programme under the Marie Skłodowska-Curie Grant
  Agreement\r\nNo. 101034413. I thank the referee for many helpful comments."
article_processing_charge: Yes (in subscription journal)
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. Some effectivity results for primitive divisors of elliptic divisibility 
    sequences. <i>Pacific Journal of Mathematics</i>. 2023;325(2):331-351. doi:<a
    href="https://doi.org/10.2140/pjm.2023.325.331">10.2140/pjm.2023.325.331</a>
  apa: Verzobio, M. (2023). Some effectivity results for primitive divisors of elliptic
    divisibility  sequences. <i>Pacific Journal of Mathematics</i>. Mathematical Sciences
    Publishers. <a href="https://doi.org/10.2140/pjm.2023.325.331">https://doi.org/10.2140/pjm.2023.325.331</a>
  chicago: Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic
    Divisibility  Sequences.” <i>Pacific Journal of Mathematics</i>. Mathematical
    Sciences Publishers, 2023. <a href="https://doi.org/10.2140/pjm.2023.325.331">https://doi.org/10.2140/pjm.2023.325.331</a>.
  ieee: M. Verzobio, “Some effectivity results for primitive divisors of elliptic
    divisibility  sequences,” <i>Pacific Journal of Mathematics</i>, vol. 325, no.
    2. Mathematical Sciences Publishers, pp. 331–351, 2023.
  ista: Verzobio M. 2023. Some effectivity results for primitive divisors of elliptic
    divisibility  sequences. Pacific Journal of Mathematics. 325(2), 331–351.
  mla: Verzobio, Matteo. “Some Effectivity Results for Primitive Divisors of Elliptic
    Divisibility  Sequences.” <i>Pacific Journal of Mathematics</i>, vol. 325, no.
    2, Mathematical Sciences Publishers, 2023, pp. 331–51, doi:<a href="https://doi.org/10.2140/pjm.2023.325.331">10.2140/pjm.2023.325.331</a>.
  short: M. Verzobio, Pacific Journal of Mathematics 325 (2023) 331–351.
date_created: 2023-01-16T11:46:19Z
date_published: 2023-11-03T00:00:00Z
date_updated: 2023-12-13T11:18:14Z
day: '03'
ddc:
- '510'
department:
- _id: TiBr
doi: 10.2140/pjm.2023.325.331
ec_funded: 1
external_id:
  arxiv:
  - '2001.02987'
  isi:
  - '001104766900001'
file:
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  creator: dernst
  date_created: 2023-11-13T09:50:41Z
  date_updated: 2023-11-13T09:50:41Z
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has_accepted_license: '1'
intvolume: '       325'
isi: 1
issue: '2'
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
page: 331-351
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
  call_identifier: H2020
  grant_number: '101034413'
  name: 'IST-BRIDGE: International postdoctoral program'
publication: Pacific Journal of Mathematics
publication_identifier:
  eissn:
  - 0030-8730
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Some effectivity results for primitive divisors of elliptic divisibility  sequences
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 325
year: '2023'
...