Multiples in the Fibonacci series

Prove that for any positive K, every Kth number in the Fibonacci sequence is a multiple of the Kth number in the Fibonacci sequence.

More formally, for any natural number n, let F(n) denote Fibonacci number n.  That is, F(0) = 0, F(1) = 1, and F(n+2) = F(n+1) + F(n).  Prove that for any positive K and natural n, F(n*K) is a multiple of F(K).

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ronret45 Expert Asked on 1st August 2015 in Microsoft Interview Puzzles.
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    sorry my browser crashes a lot so a picture is given of solution

    Yodha Expert Answered on 8th February 2016.
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