{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T04:36:44Z","timestamp":1648528604461},"reference-count":30,"publisher":"Wiley","license":[{"start":{"date-parts":[[2010,2,1]],"date-time":"2010-02-01T00:00:00Z","timestamp":1264982400000},"content-version":"unspecified","delay-in-days":396,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2009]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, <jats:italic>u<\/jats:italic><jats:sup>3<\/jats:sup> + <jats:italic>v<\/jats:italic><jats:sup>3<\/jats:sup> = <jats:italic>m<\/jats:italic>, with <jats:italic>m<\/jats:italic> cube-free, all the terms beyond the first have a primitive divisor.<\/jats:p>","DOI":"10.1112\/s1461157000000024","type":"journal-article","created":{"date-parts":[[2013,8,6]],"date-time":"2013-08-06T07:42:44Z","timestamp":1375774964000},"page":"54-81","source":"Crossref","is-referenced-by-count":2,"title":["Primitive Divisors on Twists of Fermat's Cubic"],"prefix":"10.1112","volume":"12","author":[{"given":"Graham","family":"Everest","sequence":"first","affiliation":[]},{"given":"Patrick","family":"Ingram","sequence":"additional","affiliation":[]},{"given":"Shaun","family":"Stevens","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2010,2,1]]},"reference":[{"key":"S1461157000000024_ref023","doi-asserted-by":"publisher","DOI":"10.1007\/BF01389220"},{"key":"S1461157000000024_ref014","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2006.08.007"},{"key":"S1461157000000024_ref025","doi-asserted-by":"publisher","DOI":"10.1007\/s00229-004-0468-7"},{"key":"S1461157000000024_ref030","doi-asserted-by":"publisher","DOI":"10.1007\/BF01692444"},{"key":"S1461157000000024_ref029","doi-asserted-by":"publisher","DOI":"10.2307\/2371930"},{"key":"S1461157000000024_ref028","doi-asserted-by":"publisher","DOI":"10.1016\/0022-314X(88)90019-4"},{"key":"S1461157000000024_ref026","first-page":"1","article-title":"The sign of an elliptic divisibility sequence","volume":"21","author":"Silverman","year":"2006","journal-title":"J. Ramanujan Math. Soc."},{"key":"S1461157000000024_ref003","first-page":"75","article-title":"Existence of primitive divisors of Lucas and Lehmer numbers","volume":"539","author":"Bilu","year":"2001","journal-title":"J. reine angew. Math."},{"key":"S1461157000000024_ref024","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"S1461157000000024_ref004","doi-asserted-by":"publisher","DOI":"10.1006\/jnth.1999.2430"},{"key":"S1461157000000024_ref010","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-07311-8"},{"key":"S1461157000000024_ref021","first-page":"27","article-title":"Primitive divisors of the expression An \u2013 Bn in algebraic number fields","volume":"268","author":"Schinzel","year":"1974","journal-title":"J. reine angew. Math."},{"key":"S1461157000000024_ref002","first-page":"70","article-title":"Taltheoretiske Unders\u00f8gelser","volume":"5","author":"Bang","year":"1886","journal-title":"Tidskrift f. Math."},{"key":"S1461157000000024_ref016","unstructured":"16. Ingram P. and Silverman J. H. , \u2018Uniform estimates for primitive divisors in elliptic divisibility sequences\u2019, to appear in a forthcoming memorial volume for Serge Lang (Springer)."},{"key":"S1461157000000024_ref013","volume-title":"American Mathematical Monthly","author":"Everest","year":"2007"},{"key":"S1461157000000024_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0196-8858(86)90023-0"},{"key":"S1461157000000024_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BF02567763"},{"key":"S1461157000000024_ref027","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-004-0608-0"},{"key":"S1461157000000024_ref007","unstructured":"7. Cremona J. E. , \u2018Elliptic Curve Data up-dated 05\u201301\u20132007\u2019, www.Warwick.ac.uk\/staff\/J.E.Cremona\/ftp\/data\/INDEX.htm"},{"key":"S1461157000000024_ref008","unstructured":"8. Elkies N. , \u2018Rational points with low canonical height\u2019, http:\/\/www.math.harvard.edu\/~elkies\/low_height.html"},{"key":"S1461157000000024_ref011","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-05-01737-0"},{"key":"S1461157000000024_ref012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jnt.2005.08.002"},{"key":"S1461157000000024_ref009","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s1-28.4.416"},{"key":"S1461157000000024_ref022","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511566042"},{"key":"S1461157000000024_ref018","unstructured":"18.MAGMA, version V2.13, University of Sydney, http:\/\/magma.maths.usyd.edu.au\/magma\/index.html."},{"key":"S1461157000000024_ref019","unstructured":"19.PARI\/GP, version 2.3.0, Bordeaux, 2005, http:\/\/pari.math.u-bordeaux.fr\/."},{"key":"S1461157000000024_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1967798"},{"key":"S1461157000000024_ref020","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511666148.024"},{"key":"S1461157000000024_ref017","doi-asserted-by":"publisher","DOI":"10.1017\/S0004972700034997"},{"key":"S1461157000000024_ref015","unstructured":"15. Ingram P. , \u2018Multiples of integral points on elliptic curves\u2019, arXiv:math.NT\/0802.2651v2."}],"container-title":["LMS Journal of Computation and Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1461157000000024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,6]],"date-time":"2019-06-06T14:28:48Z","timestamp":1559831328000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1461157000000024\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"references-count":30,"alternative-id":["S1461157000000024"],"URL":"https:\/\/doi.org\/10.1112\/s1461157000000024","relation":{},"ISSN":["1461-1570"],"issn-type":[{"value":"1461-1570","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009]]}}}