Luca, F and Ward, T orcid.org/0000-0002-8253-5767 (2016) An elliptic sequence is not a sampled linear recurrence sequence. New York Journal of Mathematics, 22. pp. 1319-1338. ISSN 1076-9803
Abstract
Let E be an elliptic curve defined over the rationals and in minimal Weierstrass form, and let P= (x₁/z₁², y₁/z₁³) be a rational point of infinite order on E, where x₁, y₁, z₁ are coprime integers. We show that the integer sequence (zn) n≥1 defined by nP= (xn/z²n, yn/z³n) for all n≥1 does not eventually coincide with (un²) n≥1 for any choice of linear recurrence sequence, (un)n≥1 with integer values.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Originally published in New York Journal of Mathematics, http://nyjm.albany.edu/j/2016/22-58.html. Reproduced in accordance with the publisher's self-archiving policy. |
Keywords: | elliptic divisibility sequence; non-torsion point; linear recurrence sequence |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 26 Oct 2016 13:09 |
Last Modified: | 13 Aug 2019 10:37 |
Published Version: | http://nyjm.albany.edu/j/2016/22-58.html |
Status: | Published |
Publisher: | State University of New York |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:106509 |