Journal of Integer Sequences, Vol. 14 (2011), Article 11.1.7

Arithmetic Progressions on Edwards Curves

Dustin Moody
Computer Security Division
National Institute of Standards and Technology (NIST)
100 Bureau Drive
Gaithersburg, MD 20899-8930


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.

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Received December 13 2010; revised version received January 25 2011. Published in Journal of Integer Sequences, February 8 2011.

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