1. $F(1) + F(2) + F(3) + ... + F(n) = F(n + 2) - 1$
2. $F(1)^2 + F(2)^2 + F(3)^2 + ... + F(n)^2 = F(n)F(n + 1)$
3. $F(1) + F(3) + F(5) + ... + F(2n - 1) = F(2n)$
4. $F(2) + F(4) + F(6) + ... + F(2n) = F(2n + 1) - 1$
5. $F(n) = F(m)F(n - m + 1) + F(m - 1)F(n - m)$ $(n \ge m)$
6. $F(n - 1)F(n + 1) = F(n)^2 + (-1)^n$
7. $gcd(F(n), F(m)) = F(gcd(n, m))$
8. $n\;|\;m \Leftrightarrow F(n)\;|\;F(m)$