On sequences of consecutive squares on elliptic curves

Mohamed Kamel, Mohammad Sadek

Let $C$ be an elliptic curve defined over $\mathbb{Q}$ by the equation $y^2=x^3+Ax+B$ where $A,B\in \mathbb{Q}$. A sequence of rational points $(x_i,y_i)\in C(\mathbb Q),\,i=1,2,\ldot…