lean_workbook_plus_63532

Let $(u_n)$ be a sequence that : $u_1=1; u_2=12; u_{n+1}=\dfrac{(u_n+5)^2}{u_{n-1}}$. Prove that: i) $u_n \in \mathbb{Z}^+, \forall n \in \mathbb{Z}.$ ii) $\sqrt{u_{2015}}+\sqrt{3u_{2016}} \in \mathbb{Z}^+$