Izvorni znanstveni članak

https://doi.org/10.3336/gm.52.1.01

Geometric progressions on elliptic curves

Abdoul Aziz Ciss orcid.org/0000-0001-5941-4687 ; Laboratoire de Traitement de l'Information et Systèmes Intelligents,, École Polytechnique de Thiès, BP A10 Thiès, Sénégal
Dustin Moody ; National Institute of Standards and Technology (NIST), 100 Bureau Drive, Gaithersburg, 20899-8930, USA

Sažetak

In this paper, we look at long geometric progressions on different models of elliptic curves, namely Weierstrass curves, Edwards and twisted Edwards curves, Huff curves and general quartics curves. By a geometric progression on an elliptic curve, we mean the existence of rational points on the curve whose x-coordinates (or y-coordinates) are in geometric progression. We find infinite families of twisted Edwards curves and Huff curves with geometric progressions of length 5, an infinite family of Weierstrass curves with 8-term progressions, as well as infinite families of quartic curves containing 10-term geometric progressions.

Ključne riječi

Arithmetic progression; geometric progression; elliptic curves

Hrčak ID:

183113

URI

https://hrcak.srce.hr/183113

Datum izdavanja:

21.6.2017.

Posjeta: 1.017 *