text: fibonacci numbers? show that, for any two elements m and n in n, gcd(f_(m), f_(n)) = f_gcd(m,n)   i know this is a simple proof, but i can't figure it out.  can anyone help? i know that the proof involves induction...  so for your base step you have gcd(1,1)=f(gcd(1,2))=1 is true.  for the inductive step you will need that fn + f(n+1)=f(n+2).