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Math Help - Fibonacci Numbers

  1. #1
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    Fibonacci Numbers

    Here is a question from our problem set...


    FIbonacci numbers are defined as F0=0; F1=1, and for all k >= 2 Fk = Fk-1 + Fk-2. Use strong induction to prove the following
    property of Fibonacci numbers: Fn+m-2 = FnFm-1 + Fn-1Fm-2. Here n>=2 , m>=2. Please point out the part of the proof where you had to use strong induction.

    Hint: you should do induction on n only and assume that m is fixed. The
    other way around (induction on m with n fixed) should work as well, but you
    cannot do induction on both.
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  2. #2
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    Write the induction statement, i.e., the proposition P(n) such that the problem asks you to prove "for all n >= 2, P(n)".

    Then prove the base case, i.e., P(2). Posting the results here would stimulate others to help you further.
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