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Arithmetic Progressions on Edwards Curves



Dustin Moody


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.
Journal of Integer Sequences


elliptic curves, arithmetic progressions, Edwards curves


Moody, D. (2011), Arithmetic Progressions on Edwards Curves, Journal of Integer Sequences, [online], (Accessed May 27, 2024)


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Created February 8, 2011, Updated February 19, 2017