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Math Help - Proof of Divisibilty propery of Fibonaccia numbers.

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    Proof of Divisibilty propery of Fibonaccia numbers.

    I'm struggling with understanding part of this proof.

    It makes use of this relationship.

    F_{m + n} = F_{m-1}F_n + F_mF_{n + 1}

    We are supposing that F_m is dvisible by F_n and we have just shown that F_{nq} is divisible by F_n. We are trying to proove that m is divisible by n.

    So suppose m = nq + r

    We have F_m = F_{nq+r} = F_{nq-1}F_{r} + F_{nq}F_{r+1}

    As F_{nq} is divisible by  F_n and as F_m is divisible by F_n, it follows that F_n divides F_{nq-1}F_r

    It does? Doesn't the fact that F_{nq} alone mean that F_n divides F_{nq-1}F_r? Why do we have to bother with F_m?

    Then we have

    if gcd(F_{nq-1}, F_n) = 1 we know by Euclid's Lemma that  F_n divides  F_r. I thought this only work with a prime number? How do we know one of them is prime?
    Last edited by alyosha2; December 2nd 2013 at 07:31 AM.
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