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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.
Moody, D.
(2011),
Arithmetic Progressions on Edwards Curves, Journal of Integer Sequences, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=907596
(Accessed October 20, 2025)