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    Hogatt's Theorem Proof

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    Prove Hogatt's Theorem:

    Any integer number can be written as a sum of terms of Fibonacci series.

    See attached file for full problem description.

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    Please see the attached file for the full solution.

    Hogatt's theorem states that every positive integer can be expressed as a sum of distinct Fibonacci numbers.
    Fibonacci numbers satisfy:

    We prove ...

    Solution Summary

    The solution shows an elegant proof to Hogatt's Theorem.