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The Zeckendorf Decomposition of Certain Classes of Integers

In: Applications of Fibonacci Numbers

Author

Listed:
  • Piero Filipponi
  • Herta T. Freitag

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.

Suggested Citation

  • Piero Filipponi & Herta T. Freitag, 1996. "The Zeckendorf Decomposition of Certain Classes of Integers," Springer Books, in: Gerald E. Bergum & Andreas N. Philippou & Alwyn F. Horadam (ed.), Applications of Fibonacci Numbers, pages 123-135, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-0223-7_11
    DOI: 10.1007/978-94-009-0223-7_11
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