{"external_id":{"arxiv":["1906.00632"]},"article_type":"original","volume":209,"extern":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1906.00632"}],"status":"public","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"}],"intvolume":"       209","date_updated":"2023-05-10T11:14:56Z","quality_controlled":"1","day":"01","issue":"4","title":"Primitive divisors of sequences associated to elliptic curves","month":"04","_id":"12310","publication_identifier":{"issn":["0022-314X"]},"doi":"10.1016/j.jnt.2019.09.003","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>","ista":"Verzobio M. 2020. Primitive divisors of sequences associated to elliptic curves. Journal of Number Theory. 209(4), 378–390.","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.","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>."},"type":"journal_article","keyword":["Algebra and Number Theory"],"oa_version":"Preprint","publisher":"Elsevier","scopus_import":"1","oa":1,"publication_status":"published","author":[{"id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","last_name":"Verzobio","full_name":"Verzobio, Matteo","first_name":"Matteo","orcid":"0000-0002-0854-0306"}],"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"378-390","date_created":"2023-01-16T11:45:07Z","publication":"Journal of Number Theory","article_processing_charge":"No","date_published":"2020-04-01T00:00:00Z","year":"2020"}