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Geometric Progressions on Elliptic Curves

Published

Author(s)

Abdoul Aziz Ciss, Dustin Moody

Abstract

In this paper, we look at long geometric progressions on different model 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-coordinate (or y-coordinate) 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.
Citation
GLASNIK MATEMATICKI
Volume
52
Issue
1

Keywords

arithmetic progressions, elliptic curve
Created June 13, 2017, Updated November 10, 2018