On sequences of consecutive squares on elliptic curves

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≥ 5