Abstract
Zeckendorf’s Theorem [14] for Fibonacci numbers, which is also given in Lekkerkerker [12], is stated by Brown [1], [2] for an integer N > 0 and a sequence {un} (where u n = F n + 1, the (n + l)th Fibonacci number, n ≥ 1) as follows: Zeckendorf’s Theorem: Every positive integer N has one and only one representation in the form
where each α i is a binary digit (i.e., with value 0 or 1) and
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References
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© 1993 Springer Science+Business Media Dordrecht
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Horadam, A.F. (1993). Zeckendorf Representations of Positive and Negative Integers by Pell Numbers. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2058-6_29
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DOI: https://doi.org/10.1007/978-94-011-2058-6_29
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