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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| Tipo de documento: | artigo |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universidad Autónoma de Madrid |
| Repositório: | Biblos-e Archivo. Repositorio Institucional de la UAM |
| Idioma: | inglês |
| OAI Identifier: | oai:repositorio.uam.es:10486/711220 |
| Acesso em linha: | http://hdl.handle.net/10486/711220 https://dx.doi.org/10.4064/aa167-2-2 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Arithmetic Progression Elliptic Curves Edwards Curves Matemáticas |
| Resumo: | 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 |
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