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

Geometric progressions on elliptic curves

Abdoul Aziz Ciss   ORCID icon 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

Puni tekst: engleski, pdf (120 KB) str. 1-10 preuzimanja: 269* citiraj
APA 6th Edition
Ciss, A.A. i Moody, D. (2017). Geometric progressions on elliptic curves. Glasnik matematički, 52 (1), 1-10. https://doi.org/10.3336/gm.52.1.01
MLA 8th Edition
Ciss, Abdoul Aziz i Dustin Moody. "Geometric progressions on elliptic curves." Glasnik matematički, vol. 52, br. 1, 2017, str. 1-10. https://doi.org/10.3336/gm.52.1.01. Citirano 20.09.2020.
Chicago 17th Edition
Ciss, Abdoul Aziz i Dustin Moody. "Geometric progressions on elliptic curves." Glasnik matematički 52, br. 1 (2017): 1-10. https://doi.org/10.3336/gm.52.1.01
Harvard
Ciss, A.A., i Moody, D. (2017). 'Geometric progressions on elliptic curves', Glasnik matematički, 52(1), str. 1-10. https://doi.org/10.3336/gm.52.1.01
Vancouver
Ciss AA, Moody D. Geometric progressions on elliptic curves. Glasnik matematički [Internet]. 2017 [pristupljeno 20.09.2020.];52(1):1-10. https://doi.org/10.3336/gm.52.1.01
IEEE
A.A. Ciss i D. Moody, "Geometric progressions on elliptic curves", Glasnik matematički, vol.52, br. 1, str. 1-10, 2017. [Online]. https://doi.org/10.3336/gm.52.1.01

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

Posjeta: 397 *