[{"article_processing_charge":"No","issue":"4","arxiv":1,"date_published":"2020-04-01T00:00:00Z","_id":"12310","abstract":[{"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.","lang":"eng"}],"oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1906.00632","open_access":"1"}],"publication_status":"published","volume":209,"year":"2020","oa_version":"Preprint","article_type":"original","publication_identifier":{"issn":["0022-314X"]},"external_id":{"arxiv":["1906.00632"]},"scopus_import":"1","date_updated":"2023-05-10T11:14:56Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"378-390","date_created":"2023-01-16T11:45:07Z","month":"04","extern":"1","publisher":"Elsevier","status":"public","intvolume":"       209","publication":"Journal of Number Theory","quality_controlled":"1","title":"Primitive divisors of sequences associated to elliptic curves","citation":{"short":"M. Verzobio, Journal of Number Theory 209 (2020) 378–390.","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>","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>","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.","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>.","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>."},"author":[{"full_name":"Verzobio, Matteo","first_name":"Matteo","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","orcid":"0000-0002-0854-0306"}],"type":"journal_article","day":"01","doi":"10.1016/j.jnt.2019.09.003","keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}]},{"volume":96,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"publication_status":"published","_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."}],"date_published":"2002-10-02T00:00:00Z","issue":"2","article_processing_charge":"No","date_updated":"2023-07-26T12:15:14Z","user_id":"ea97e931-d5af-11eb-85d4-e6957dddbf17","scopus_import":"1","publication_identifier":{"issn":["0022-314X"]},"publist_id":"7708","article_type":"original","year":"2002","oa_version":"Published Version","quality_controlled":"1","publication":"Journal of Number Theory","intvolume":"        96","status":"public","publisher":"Academic Press","extern":"1","month":"10","date_created":"2018-12-11T11:45:11Z","page":"293 - 318","language":[{"iso":"eng"}],"doi":"10.1006/jnth.2002.2800","day":"02","author":[{"full_name":"Browning, Timothy D","first_name":"Timothy D","last_name":"Browning","id":"35827D50-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-8314-0177"}],"type":"journal_article","citation":{"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>","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>","short":"T.D. Browning, Journal of Number Theory 96 (2002) 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>.","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.","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>."},"title":"Equal Sums of Two kth Powers"}]