Geodesic
Arithmetic progressions on Edwards curves
Journal of integer sequences, Tome 14 (2011) no. 1.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We look at arithmetic progressions on elliptic curves known as Edwards curves. By an arithmetic progression on an elliptic curve, we mean that the $x$-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has found arithmetic progressions on Weierstrass curves, quartic curves, and genus 2 curves. We find an infinite number of Edwards curves with an arithmetic progression of length 9.
Classification : 11G05, 11B25
Keywords: arithmetic progression, elliptic curve, edwards curve 
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     author = {Moody, Dustin},
     title = {Arithmetic progressions on {Edwards} curves},
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Moody, Dustin. Arithmetic progressions on Edwards curves. Journal of integer sequences, Tome 14 (2011) no. 1. http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a7/