Possible Duplicate:
Recurrence relation, Fibonacci numbers
could someone possibly help me prove. thankyou.
$(a)$ Consider the recurrence relation $a_{n+2}a_n = a^2 _{n+1} + 2$ with $a_1 = a_2 = 1$.
prove $a_n$ and $a_{n+1}$ are coprime for $n \in \mathbb N$
so far i have:
$a_1 = a_2 = 1$
$a_3 = 3$
$a_4 = 11$
$a_5 = 41$