Diophantine Equation $x_1^3-x_2^2{x}_1+1=0$ over number fields

Pinki Khatun

Let $\mathbb{K}=\mathbb{Q}(\sqrt{-d})$, where $d$ is a positive square-free integer, or let $\mathbb{K}=\mathbb{Q}(\sqrt{2})$, and denote by ${\mathcal{O}}_{\mathbb{K}}$ the ring of in…