Question 2
Find all integers $n \geq 3$ for which there exist real numbers $a_1, a_2, \dots, a_n$ satisfying $$
a_i a_{i+1} +1 = a_{i+2}
$$ for $i=1,2, \dots, n$, where indices are taken modulo $n$.
a_i a_{i+1} +1 = a_{i+2}
$$ for $i=1,2, \dots, n$, where indices are taken modulo $n$.