On Simultaneous Arithmetic Progressions on Elliptic Curves

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.

Keywords:

• Primary 11G05
• Secondary 14H52, 11B25
• Elliptic curves
• arithmetic progressions