{"abstract":[{"text":"Take a rational elliptic curve defined by the equation y2=x3+ax in minimal form and consider the sequence Bn of the denominators of the abscissas of the iterate of a non-torsion point. We show that B5m has a primitive divisor for every m. Then, we show how to generalize this method to the terms of the form Bmp with p a prime congruent to 1 modulo 4.","lang":"eng"}],"date_updated":"2023-05-08T11:58:14Z","language":[{"iso":"eng"}],"publisher":"Institute of Mathematics, Polish Academy of Sciences","scopus_import":"1","author":[{"orcid":"0000-0002-0854-0306","last_name":"Verzobio","id":"7aa8f170-131e-11ed-88e1-a9efd01027cb","first_name":"Matteo","full_name":"Verzobio, Matteo"}],"intvolume":"       198","doi":"10.4064/aa191016-30-7","_id":"12309","publication":"Acta Arithmetica","external_id":{"arxiv":["2001.09634"]},"date_created":"2023-01-16T11:44:54Z","status":"public","citation":{"apa":"Verzobio, M. (2021). Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>","short":"M. Verzobio, Acta Arithmetica 198 (2021) 129–168.","ama":"Verzobio M. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. <i>Acta Arithmetica</i>. 2021;198(2):129-168. doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>","chicago":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>. Institute of Mathematics, Polish Academy of Sciences, 2021. <a href=\"https://doi.org/10.4064/aa191016-30-7\">https://doi.org/10.4064/aa191016-30-7</a>.","mla":"Verzobio, Matteo. “Primitive Divisors of Elliptic Divisibility Sequences for Elliptic Curves with J=1728.” <i>Acta Arithmetica</i>, vol. 198, no. 2, Institute of Mathematics, Polish Academy of Sciences, 2021, pp. 129–68, doi:<a href=\"https://doi.org/10.4064/aa191016-30-7\">10.4064/aa191016-30-7</a>.","ista":"Verzobio M. 2021. Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728. Acta Arithmetica. 198(2), 129–168.","ieee":"M. Verzobio, “Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728,” <i>Acta Arithmetica</i>, vol. 198, no. 2. Institute of Mathematics, Polish Academy of Sciences, pp. 129–168, 2021."},"day":"04","year":"2021","publication_status":"published","oa":1,"article_type":"original","quality_controlled":"1","article_processing_charge":"No","title":"Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728","publication_identifier":{"issn":["0065-1036","1730-6264"]},"oa_version":"Preprint","volume":198,"page":"129-168","issue":"2","keyword":["Algebra and Number Theory"],"month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","extern":"1","type":"journal_article","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2001.09634","open_access":"1"}],"date_published":"2021-01-04T00:00:00Z"}