Glasnik matematički, Vol. 52 No. 1, 2017.
Izvorni znanstveni članak
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
Sažetak
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.
Ključne riječi
Elliptic curves; rational points, sequences of consecutive squares
Hrčak ID:
183122
URI
Datum izdavanja:
21.6.2017.
Posjeta: 1.387 *