Original scientific paper

https://doi.org/10.3336/gm.54.1.04

Rational sequences on different models of elliptic curves

Gamze Savaş Çelik ; Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey
Mohammad Sadek orcid.org/0000-0002-2189-5603 ; Faculty of Engineering and Natural Sciences, Sabancı University, 34956 Tuzla, Istanbul, Turkey
Gökhan Soydan orcid.org/0000-0002-6321-4132 ; Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey

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 |S| 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.

Keywords

Elliptic curve; Edwards curve; Huff curve; rational sequence; rational point

Hrčak ID:

220842

URI

https://hrcak.srce.hr/220842

Publication date:

7.6.2019.

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