Sequences of consecutive squares on quartic elliptic curves

Mohammad Sadek, Mohamed Kamel

Let $C:y^2=a{x}^4+b{x}^2+c$, be an elliptic curve defined over $\mathbb{Q}$. A set of rational points $(x_i,y_i)\in C(\mathbb{Q})$, $i=1,2,\cdots ,$ is said to be a sequence of consecut…