Question 4
The sequence $(a_n)$ is defined by $a_0=1$, $a_1=3$ and
$$a_{n+2}=1+\left\lfloor\frac{a_{n+1}^2}{a_n}\right\rfloor\quad(n\ge0).$$
Prove that $a_na_{n+2}-a_{n+1}^2=2^n$ for every integer $n\ge0$.
$$a_{n+2}=1+\left\lfloor\frac{a_{n+1}^2}{a_n}\right\rfloor\quad(n\ge0).$$
Prove that $a_na_{n+2}-a_{n+1}^2=2^n$ for every integer $n\ge0$.