---
_id: '12310'
abstract:
- lang: eng
  text: Let  be a sequence of points on an elliptic curve defined over a number field
    K. In this paper, we study the denominators of the x-coordinates of this sequence.
    We prove that, if Q is a torsion point of prime order, then for n large enough
    there always exists a primitive divisor. Later on, we show the link between the
    study of the primitive divisors and a Lang-Trotter conjecture. Indeed, given two
    points P and Q on the elliptic curve, we prove a lower bound for the number of
    primes p such that P is in the orbit of Q modulo p.
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 sequences associated to elliptic curves.
    <i>Journal of Number Theory</i>. 2020;209(4):378-390. doi:<a href="https://doi.org/10.1016/j.jnt.2019.09.003">10.1016/j.jnt.2019.09.003</a>
  apa: Verzobio, M. (2020). Primitive divisors of sequences associated to elliptic
    curves. <i>Journal of Number Theory</i>. Elsevier. <a href="https://doi.org/10.1016/j.jnt.2019.09.003">https://doi.org/10.1016/j.jnt.2019.09.003</a>
  chicago: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic
    Curves.” <i>Journal of Number Theory</i>. Elsevier, 2020. <a href="https://doi.org/10.1016/j.jnt.2019.09.003">https://doi.org/10.1016/j.jnt.2019.09.003</a>.
  ieee: M. Verzobio, “Primitive divisors of sequences associated to elliptic curves,”
    <i>Journal of Number Theory</i>, vol. 209, no. 4. Elsevier, pp. 378–390, 2020.
  ista: Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves.
    Journal of Number Theory. 209(4), 378–390.
  mla: Verzobio, Matteo. “Primitive Divisors of Sequences Associated to Elliptic Curves.”
    <i>Journal of Number Theory</i>, vol. 209, no. 4, Elsevier, 2020, pp. 378–90,
    doi:<a href="https://doi.org/10.1016/j.jnt.2019.09.003">10.1016/j.jnt.2019.09.003</a>.
  short: M. Verzobio, Journal of Number Theory 209 (2020) 378–390.
date_created: 2023-01-16T11:45:07Z
date_published: 2020-04-01T00:00:00Z
date_updated: 2023-05-10T11:14:56Z
day: '01'
doi: 10.1016/j.jnt.2019.09.003
extern: '1'
external_id:
  arxiv:
  - '1906.00632'
intvolume: '       209'
issue: '4'
keyword:
- Algebra and Number Theory
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1906.00632
month: '04'
oa: 1
oa_version: Preprint
page: 378-390
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Primitive divisors of sequences associated to elliptic curves
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 209
year: '2020'
...
---
_id: '204'
abstract:
- lang: eng
  text: Let k⩾5 be an integer, and let x⩾1 be an arbitrary real number. We derive
    a bound[Formula presented] for the number of positive integers less than or equal
    to x which can be represented as a sum of two non-negative coprime kth powers,
    in essentially more than one way.
article_processing_charge: No
article_type: original
author:
- first_name: Timothy D
  full_name: Browning, Timothy D
  id: 35827D50-F248-11E8-B48F-1D18A9856A87
  last_name: Browning
  orcid: 0000-0002-8314-0177
citation:
  ama: Browning TD. Equal Sums of Two kth Powers. <i>Journal of Number Theory</i>.
    2002;96(2):293-318. doi:<a href="https://doi.org/10.1006/jnth.2002.2800">10.1006/jnth.2002.2800</a>
  apa: Browning, T. D. (2002). Equal Sums of Two kth Powers. <i>Journal of Number
    Theory</i>. Academic Press. <a href="https://doi.org/10.1006/jnth.2002.2800">https://doi.org/10.1006/jnth.2002.2800</a>
  chicago: Browning, Timothy D. “Equal Sums of Two Kth Powers.” <i>Journal of Number
    Theory</i>. Academic Press, 2002. <a href="https://doi.org/10.1006/jnth.2002.2800">https://doi.org/10.1006/jnth.2002.2800</a>.
  ieee: T. D. Browning, “Equal Sums of Two kth Powers,” <i>Journal of Number Theory</i>,
    vol. 96, no. 2. Academic Press, pp. 293–318, 2002.
  ista: Browning TD. 2002. Equal Sums of Two kth Powers. Journal of Number Theory.
    96(2), 293–318.
  mla: Browning, Timothy D. “Equal Sums of Two Kth Powers.” <i>Journal of Number Theory</i>,
    vol. 96, no. 2, Academic Press, 2002, pp. 293–318, doi:<a href="https://doi.org/10.1006/jnth.2002.2800">10.1006/jnth.2002.2800</a>.
  short: T.D. Browning, Journal of Number Theory 96 (2002) 293–318.
date_created: 2018-12-11T11:45:11Z
date_published: 2002-10-02T00:00:00Z
date_updated: 2023-07-26T12:15:14Z
day: '02'
doi: 10.1006/jnth.2002.2800
extern: '1'
intvolume: '        96'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '10'
oa_version: Published Version
page: 293 - 318
publication: Journal of Number Theory
publication_identifier:
  issn:
  - 0022-314X
publication_status: published
publisher: Academic Press
publist_id: '7708'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Equal Sums of Two kth Powers
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: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 96
year: '2002'
...