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Math Help - Fibonacci numbers.

  1. #1
    Senior Member I-Think's Avatar
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    Fibonacci numbers.

    The Fibonacci numbers are defined by F_0=0,  F_1=1 and F_n=F_{n-1}+F_{n-2}
    Prove if 2|F_n, then 3|n

    This is one of those times where it's easy to see intuitively, it's hard to see formally.
    Considering the Fibonacci sequence
    0,1,1,2,3,5,8,13,21,36...

    It falls into a pattern of
    E,O,O,E,O,O,E,O,O,E,...

    From, as the first term F_0 is even, it's clear to see that every third term beginning from F_1 is divisible by 3, as it is the sum of the 2 previous numbers which are odd.

    But this just scaffolding, scrap work.
    Any tips on how to codify this formally?
    Last edited by mr fantastic; October 25th 2010 at 05:37 PM. Reason: Re-titled.
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  2. #2
    Pim
    Pim is offline
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    Given the recursive nature of Fibonacci numbers, a proof by induction seems to be the logical way to go. Have you considered that?
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