For the fibonacci numbers fn prove that the gcd(fn, fn+1)=1 for all n greater than or equal to 1. Do I need to maybe do induction?

Question

anonymous · Answer

lol fibonacci = induction

anonymous · Answer

$$gcd(f_{n+1}, f_{n+1})=gcd(f_{n+1},f_{n+1}+f_{n+2})$$ is probably a good place to start, since $f_n$ is the fibonacci sequence

anonymous · Answer

damn typo!

anonymous · Answer

$$gcd(f_{n+1}, f_{n+2})=gcd(f_{n+1},f_{n+1}+f_{n+2})$$ is more like it

anonymous · Answer

damn another tyopo
i must be tired let me try again

anonymous · Answer

$$gcd(f_{n+1}, f_{n+2})=gcd(f_{n+1},f_{n}+f_{n+1})$$ whew  that is what i was trying to point out
that is because $f_{n+2}=f_n+f_{n+1}$

anonymous · Answer

it's ok at least you are trying to help hahaha! Thanks for all of your help tonight