# Thread: Help me to prove that F(n) and F(m) are prime to each other.

1. ## Help me to prove that F(n) and F(m) are prime to each other.

, ,m is different from n (m!=n), they are integers and m>=0 , n>=0 . I know i have to prove that gcd(F(n),F(m))=1. I've been trying to prove for 2 days already and now i'm on the verge of giving up ... I'd be glad to see solution and explanation.

2. ## Re: Help me to prove that F(n) and F(m) are prime to each other.

Do you know (or can you prove) the relation

$F(n) = F(0)F(1) \cdots F(n-1) + 2$

? Then show how to use this equation to derive the desired result.

3. ## Re: Help me to prove that F(n) and F(m) are prime to each other.

Yes,I know and can prove it.