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

**Gromour** · November 11th 2012, 02:20 AM

,

Help me to prove that F(n) and F(m) are prime to each other.-clip_image004.gif

,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.

**Petek** · November 11th 2012, 03:28 AM

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.

**Gromour** · November 11th 2012, 03:33 AM

Yes,I know and can prove it.

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

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