On geometric progressions on hyperelliptic curves

Mohamed Alaa, Mohammad Sadek

Let $C$ be a hyperelliptic curve over $\mathbb{Q}$ described by $y^2=a_0{x}^n+a_1{x}^{n-1}+\dots +a_n$, $a_i\in \mathbb{Q}$. The points $P_i=(x_i,y_i)\in C(\mathbb{Q})$, $i=1,2,...,…