Question 6
For all positive integral $n$, $u_{n+1}=u_n(u_{n-1}^2-2)-u_1$, $u_0=2$, and $u_1=2\frac12$. Prove that
$$3\log_2[u_n]=2^n-(-1)^n,$$
where $[x]$ is the integral part of $x$.
$$3\log_2[u_n]=2^n-(-1)^n,$$
where $[x]$ is the integral part of $x$.