Abstract
That any positive integer N can be represented as a sum of distinct nonconsecutive Fibonacci numbers F i is a well-known fact. Apart from the equivalent use of F 2 instead of F 1, such a representation is unique [1] and is commonly refereed to as the Zeckeniorf Decomposition (or Representation) of N [ZD(N), in brief].
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References
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© 1998 Springer Science+Business Media Dordrecht
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Filipponi, P., Freitag, H.T. (1998). Some Probabilistic Aspects of the Zeckendorf Decomposition of Integers. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5020-0_14
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DOI: https://doi.org/10.1007/978-94-011-5020-0_14
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