**1,1,2,3,5,8,13...**
Given basic Fibonacci sequence (as above) with **a**_{1}=1 and **a**_{2}=1 evaluate the GCD of **a**_{770} and **a**_{1000}.

Here, we express the GCD of a and b as (a,b), and the i'th F number as F(i).

We use the remarkable theorem: (F(a),F(b)) = F(a,b)

Here, a = 770 = 2 * 5 * 7 * 11 and b = 1000 = 2^3 * 5^3

so... (a,b) = 10 and thus, F(10) = 55, is our answer.

*Edited on ***June 10, 2020, 2:46 pm**