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Thread: Fibonacci Proof

  1. November 5th 2009, 05:00 AM #1
    sirellwood
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    Fibonacci Proof

    Hi all

    Prove that every 4th Fibonacci number is divisible by 3, that is 3|f4n, for all n>=1.
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  2. November 5th 2009, 05:43 AM #2
    tonio
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    Quote Originally Posted by sirellwood View Post
    Hi all

    Prove that every 4th Fibonacci number is divisible by 3, that is 3|f4n, for all n>=1.

    Induction and some patience: F_{4n}=F_{4n-1}+F_{4n-2}=F_{4n-2}+F_{4n-3}+F_{4n-3}+F_{4n-4} = F_{4n-3}+F_{4n-4}+F_{4n-3}+F_{4n-3}+F_{4n-4}=...

    Tonio

    Pd. The solution's already present in the rightmost expression above.
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  3. November 5th 2009, 08:08 AM #3
    sirellwood
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    Sorry, im not sure where you are going with this one?
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« Another coprime proof | Continued fraction »

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