Geodesic
On arithmetic progressions on Edwards curves
Enrique González-Jiménez1
1 Departamento de Matemáticas Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas (ICMat) Madrid, Spain
Acta Arithmetica, Tome 167 (2015) no. 2, pp. 117-132

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Let $m\in {\mathbb {Z}}_{>0}$ and $a,q\in {\mathbb {Q}}$. Denote by $\mathcal {AP}_{m}(a,q)$ the set of rational numbers $d$ such that $a,a+q,\dots ,a+(m-1)q$ form an arithmetic progression in the Edwards curve $E_d : x^2+y^2=1+dx^2 y^2$. We study the set $\mathcal {AP}_{m}(a,q)$ and we parametrize it by the rational points of an algebraic curve.
DOI : 10.4064/aa167-2-2
Keywords: mathbb mathbb denote mathcal set rational numbers dots m form arithmetic progression edwards curve study set mathcal parametrize rational points algebraic curve

Enrique González-Jiménez 1

1 Departamento de Matemáticas Universidad Autónoma de Madrid and Instituto de Ciencias Matemáticas (ICMat) Madrid, Spain 
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Enrique González-Jiménez. On arithmetic progressions on Edwards curves. Acta Arithmetica, Tome 167 (2015) no. 2, pp. 117-132. doi: 10.4064/aa167-2-2

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