Glasnik Matematicki, Vol. 54, No. 1 (2019), 53-64.

RATIONAL SEQUENCES ON DIFFERENT MODELS OF ELLIPTIC CURVES

Gamze Savaş Çelik, Mohammad Sadek and Gökhan Soydan

Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey
e-mail: gamzesavascelik@gmail.com

Faculty of Engineering and Natural Sciences, Sabancı University, 34956 Tuzla, Istanbul, Turkey
e-mail: mmsadek@sabanciuniv.edu

Department of Mathematics, Bursa Uludağ University, 16059 Bursa, Turkey
e-mail: gsoydan@uludag.edu.tr

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.

2010 Mathematics Subject Classification.   11D25, 11G05, 14G05

Key words and phrases.   Elliptic curve, Edwards curve, Huff curve, rational sequence, rational point

Full text (PDF) (free access)

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

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