On arithmetic progressions on Edwards curves
Number Theory
2015-04-09 v2 Algebraic Geometry
Abstract
Let m be a positive integer and a,q two rational numbers. Denote by AP_m(a,q) the set of rational numbers d such that a,a+q,...,a+(m-1)q form an arithmetic progression in the Edwards curve E_d:x^2+y^2=1+d x^2 y^2. We study the set AP_m(a,q) and we parametrize it by the rational points of an algebraic curve.
Keywords
Cite
@article{arxiv.1304.4361,
title = {On arithmetic progressions on Edwards curves},
author = {Enrique Gonzalez-Jimenez},
journal= {arXiv preprint arXiv:1304.4361},
year = {2015}
}