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Publication Citation: Arithmetic Progressions on Huff Curves

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Author(s): Dustin Moody;
Title: Arithmetic Progressions on Huff Curves
Published: July 23, 2012
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
Pages: pp. 111 - 116
Keywords: Diophantine equations; arithmetic progressions; elliptic curves
Research Areas: Math, Computer Security
PDF version: PDF Document Click here to retrieve PDF version of paper (342KB)