RATIONAL SEQUENCES ON DIFFERENT MODELS OF ELLIPTIC CURVES


Celik G. S. , Sadek M., SOYDAN G.

GLASNIK MATEMATICKI, vol.54, no.1, pp.53-64, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 54 Issue: 1
  • Publication Date: 2019
  • Doi Number: 10.3336/gm.54.1.04
  • Journal Name: GLASNIK MATEMATICKI
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.53-64
  • Keywords: Elliptic curve, Edwards curve, Huff curve, rational sequence, rational point, ARITHMETIC PROGRESSIONS, GEOMETRIC PROGRESSIONS
  • Bursa Uludag University Affiliated: Yes

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.