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

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

    Help me to prove that F(n) and F(m) are prime to each other.-clip_image002.gif,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.
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  2. #2
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    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.
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  3. #3
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    Re: Help me to prove that F(n) and F(m) are prime to each other.

    Yes,I know and can prove it.
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