Calculate GCD(Fib(531185354674),Fib(613570636967)) I picked this problem from here . I don't know how to solve it accurately. The number seems too to be done by any computation method.

Try and compute $\gcd(F_i,F_j)$ for some small $i$ and $j$ and see if you can spot a pattern.

Using the following three facts you can prove by induction that the pattern holds in general:

* $\gcd(F_n,F_{n-1}) = 1$.
* $F_{m+n} = F_{m+1}F_n + F_mF_{n-1}$.
* $m$ divides $n \implies F_m$ divides $F_n$.