One can prove the greatest common divisor of two fibonacci n

One can prove the greatest common divisor of two fibonacci numbers is also a fibonacci number; specifically, gcd (Fn, Fm)= Fd where d= gcd (n,m) Verify this identity in the case of gcd (F9, F12) and gcd(F15, F20)

Solution

F9 is the number 21 and F12 is the number 89

and gcd of (21,89) = 1 which is equal to F3 where 3 = gcd(9,12)

and

F15 is the number 377 and F20 is the number 4181

and gcd of (377,4181) = 1 which is not equal to F5 where 5 = gcd(15,20)