On arithmetic progressions on Edwards curves

Enrique González-Jiménez

Acta Arithmetica, Tome 168 (2015), p. 117-132 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $m \in ℤ_{> 0}$ and a,q ∈ ℚ. Denote by $_{m} (a, q)$ 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 $_{m} (a, q)$ and we parametrize it by the rational points of an algebraic curve.

Publié le : 2015-01-01

Zbl 1322.11057

EUDML-ID : urn:eudml:doc:279397

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     author = {Enrique Gonz\'alez-Jim\'enez},
     title = {On arithmetic progressions on Edwards curves},
     journal = {Acta Arithmetica},
     volume = {168},
     year = {2015},
     pages = {117-132},
     zbl = {1322.11057},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-2-2}
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Enrique González-Jiménez. On arithmetic progressions on Edwards curves. Acta Arithmetica, Tome 168 (2015) pp. 117-132. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa167-2-2/