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Arithmetic Progressions on Edwards Curves
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Dustin Moody

Computer Security Division

National Institute of Standards and Technology (NIST)

100 Bureau Drive

Gaithersburg, MD 20899-8930

USA

**Abstract:**

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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