Question 7
(CAN 5) Let $a$ be a positive integer and let $\{a_n\}$ be defined by $a_0=0$ and
$$a_{n+1}=(a_n+1)a+(a+1)a_n+2\sqrt{a(a+1)a_n(a_n+1)}\qquad(n=1,2\ldots).$$
Show that for each positive integer $n$, $a_n$ is a positive integer.
$$a_{n+1}=(a_n+1)a+(a+1)a_n+2\sqrt{a(a+1)a_n(a_n+1)}\qquad(n=1,2\ldots).$$
Show that for each positive integer $n$, $a_n$ is a positive integer.