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.
Citation: Journal of Integer Sequences
Pub Type: Journals
elliptic curves, arithmetic progressions, Edwards curves