Original scientific paper

https://doi.org/10.3336/gm.52.1.04

On sequences of consecutive squares on elliptic curves

Mohamed Kamel ; Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt
Mohammad Sadek ; Mathematics and Actuarial Science Department, American University in Cairo, AUC Avenue, New Cairo, Egypt

Abstract

Let C be an elliptic curve defined over Q by the equation y2=x3+Ax+B where A,BQ. A sequence of rational points (xi,yi) C(Q), i=1,2,…, is said to form a sequence of consecutive squares on C if the sequence of x-coordinates, xi,i=1,2,…, consists of consecutive squares. We produce an infinite family of elliptic curves C with a 5-term sequence of consecutive squares. Furthermore, this sequence consists of five independent rational points in C(Q). In particular, the rank r of C(Q) satisfies r≥ 5.

Keywords

Elliptic curves; rational points, sequences of consecutive squares

Hrčak ID:

183122

URI

https://hrcak.srce.hr/183122

Publication date:

21.6.2017.

Visits: 1.749 *