The Zeckendorf Decomposition of Certain Classes of Integers

Piero Filipponi and Herta T. Freitag

A chapter in Applications of Fibonacci Numbers, 1996, pp 123-135 from Springer

Abstract: Abstract That any positive integer N can be represented as a sum of distinct nonconsecutive Fibonacci numbers F n 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 referred to as the Zeckendorf Decomposition (or Representation) of N (ZD of N, in brief). Since the ZD of a class of integers is in general unpredictable, its discovery is always a pleasant surprise to the researcher. This fact led us to undertake this kind of investigations.

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_11

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