Geodesic
Arithmetic progressions on Edwards curves
Journal of integer sequences, Tome 14 (2011) no. 1
Zbl
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 
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/
@article{JIS_2011__14_1_a7,
     author = {Moody,  Dustin},
     title = {Arithmetic progressions on {Edwards} curves},
     journal = {Journal of integer sequences},
     year = {2011},
     volume = {14},
     number = {1},
     zbl = {1269.11055},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2011__14_1_a7/}
}
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