Çelik, Gamze Savaş and Sadek, Mohammad and Soydan, Gökhan
(2019)
*Rational sequences on different models of elliptic curves.*
Glasnik Matematicki, 54
(1).
pp. 53-64.
ISSN 0017-095X (Print) 1846-7989 (Online)

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Official URL: http://dx.doi.org/10.3336/gm.54.1.04

## Abstract

Given a set S of elements in a number field k, we discuss the existence of planar algebraic curves over k which possess rational points whose x-coordinates are exactly the elements of S. If the size vertical bar S vertical bar of S is either 4, 5, or 6, we exhibit infinite families of (twisted) Edwards curves and (general) Huff curves for which the elements of S are realized as the x-coordinates of rational points on these curves. This generalizes earlier work on progressions of certain types on some algebraic curves.

Item Type: | Article |
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Uncontrolled Keywords: | Elliptic curve; Edwards curve; Huff curve; rational sequence; rational point |

Subjects: | Q Science > QA Mathematics > QA150-272.5 Algebra |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Mohammad Sadek |

Date Deposited: | 24 Aug 2019 22:54 |

Last Modified: | 04 Aug 2023 21:09 |

URI: | https://research.sabanciuniv.edu/id/eprint/37315 |