%0 Journal Article
%T On sequences of consecutive squares on elliptic curves
%A Kamel
%A Mohamed
%A Sadek
%A Mohammad
%J -
%D 2017
%R 10.3336/gm.52.1.04
%X Sa£¿etak 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¡İ 5
%K Elliptic curves
%K rational points
%K sequences of consecutive squares
%U https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=270024