On the Representation of Integral Sequences {Fn/d} and {Ln/d} as Sums of Fibonacci Numbers and as Sums of Lucas Numbers

Herta T. Freitag and Piero Filipponi

A chapter in Applications of Fibonacci Numbers, 1988, pp 97-112 from Springer

Abstract: Abstract Based on Zeckendorf’s theorem concerning the unique sum-representation of any positive integer in terms of Fibonacci numbers as well as Lucas numbers /1/, the purpose of this study is the development of relationships which enable prediction of the NUMBER of addends in these representations. Integral sequences {Fn/d} and {Ln/d} are considered such that d, with 2 is a predetermined integer and n is subject to appropriate conditions to assure integral elements in these sequences. Restrictions on n such that Fn = 0 (mod d) can always be determined. However, for n ε{5, 8, 10, 12, 13, 15, 16, 17, 20} there does not exist an n-value such that Ln = 0 (mod d).

Keywords: Positive Integer; Nonnegative Integer; Integral Element; Geometric Series; Fibonacci Number (search for similar items in EconPapers)
Date: 1988
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-7801-1_11

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DOI: 10.1007/978-94-015-7801-1_11

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