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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.

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Solution Summary

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

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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 ...

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