Problem $12.$

Let the "Fibonacci$-2"$ numbers $g_n$ be defined as follows: $[$MLO$7-5]g_1=2,g_2=2$ and $g_{n+2}=g_{n+1}{g}_n$ for all $n1.$

$($a$)$ Calculate the first five "Fibonacci$-2"$ numbers. $[$submit$]$

$($b$)$ Show that for all ninN,$g_n=2^{f_n}.[$submit$]$