Experimental Mathematics

On Simultaneous Arithmetic Progressions on Elliptic Curves

Irene García-Selfa and José M. Tornero

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Abstract

In this paper we study elliptic curves that have a number of points whose coordinates are in arithmetic progression. We first motivate this Diophantine problem; then we prove some results, provide a number of interesting examples, and finally point out open questions that focus on the most interesting aspects of the problem for us.

Article information

Source
Experiment. Math., Volume 15, Issue 4 (2006), 471-478.

Dates
First available in Project Euclid: 5 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.em/1175789781

Mathematical Reviews number (MathSciNet)
MR2293597

Zentralblatt MATH identifier
1215.11056

Subjects
Primary: 11G05: Elliptic curves over global fields [See also 14H52]
Secondary: 14H52: Elliptic curves [See also 11G05, 11G07, 14Kxx] 11B25: Arithmetic progressions [See also 11N13]

Keywords
Elliptic curves arithmetic progressions

Citation

García-Selfa, Irene; Tornero, José M. On Simultaneous Arithmetic Progressions on Elliptic Curves. Experiment. Math. 15 (2006), no. 4, 471--478. https://projecteuclid.org/euclid.em/1175789781


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