On arithmetic progressions on Edwards curves

Assume m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an 2 2 2 arithmetic progression in the Edwards curve Ed : x + y = 1 + d x2y . In these conditions, we study the set APm(a, q) and we parametrize it by the rational points o...

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Detalles Bibliográficos
Autor: González Jiménez, Enrique
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/711220
Acceso en línea:http://hdl.handle.net/10486/711220
https://dx.doi.org/10.4064/aa167-2-2
Access Level:acceso abierto
Palabra clave:Arithmetic Progression
Elliptic Curves
Edwards Curves
Matemáticas
Descripción
Sumario:Assume m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an 2 2 2 arithmetic progression in the Edwards curve Ed : x + y = 1 + d x2y . In these conditions, we study the set APm(a, q) and we parametrize it by the rational points of an algebraic curve