On the Representation of {F kn /F n }, {F kn /L n }, {L kn /L n }, and {L kn /F n } as Zeckendorf Sums

Herta T. Freitag

A chapter in Applications of Fibonacci Numbers, 1990, pp 107-114 from Springer

Abstract: Abstract Zeckendor’s Theorem guarantees that every positive integer can be uniquely expressed as a sum of Fibonacci numbers, provided no two consecutive numbers are taken. The same holds for Lucas numbers, with the one additional condition that L2 and L0 not occur in the same representation (or else, 5 = L3 + L1 = L2 + L0). This note deals with sets of integers {F kn /F n }, {F kn /L n }, {L kn /L n }, and {L kn /F n } where n and k are positive integers obeying appropriate conditions to assure that all elements in our sequence are integral. Functions φ and λ are displayed where φ denotes the NUMBER OF addends in the FIBONACCI representation and λ the NUMBER OF LUCAS terms.

Keywords: Positive Integer; Computational Mathematic; Natural Number; Number Theory; Additional Condition (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-94-009-1910-5_11

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