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Arithmetic Progressions on Huff Curves

Published

Author(s)

Dustin Moody

Abstract

We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-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, Edwards curves, and genus 2 curves. We find an infinite number of Huff curves with an arithmetic progression of length 9.
Citation
Annales Mathematicae et Informaticae
Volume
38

Keywords

Diophantine equations, arithmetic progressions, elliptic curves

Citation

Moody, D. (2012), Arithmetic Progressions on Huff Curves, Annales Mathematicae et Informaticae, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=908329 (Accessed April 13, 2024)
Created July 23, 2012, Updated February 19, 2017