Abstract
It is well known that the Fibonacci sequence (F n ) n ≥0 defined by F0 = 0, F1 = 1, and F n +2 = n +1 +F n for all n ≥ 0 satisfies the condition F2 n − F n +1 F n −1 = (-1) n for all n ∈ N In this note, we show that — somehow conversely — if (A n ) n ≥0 is a sequence of integers such that (|A n |) n ≥0 diverges to infinity and |A2 n − A n +1 A n −1|remains bounded, then (A n ) n ≥0 is binary recurrent from some n on. An application to real quadratic units is also presented.
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References
A. Dubickas, A note on powers of Pisot numbers, Publ. Math. (Debrecen) 56 (2000), 141–143.
F. Luca, On a question of G. Kuba, Arch. Math. 74 (2000), 269–275.
M. Mignotte, A characterization of integers, Amer. Math. Monthly 84 (1977), 278–281.
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© 2001 Springer-Verlag Berlin Heidelberg
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Dress, A., Luca, F. (2001). Unbounded Integer Sequences (A n ) n≥0 with A n+1A n−1− A 2 n Bounded are of Fibonacci Type. In: Betten, A., Kohnert, A., Laue, R., Wassermann, A. (eds) Algebraic Combinatorics and Applications. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59448-9_7
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DOI: https://doi.org/10.1007/978-3-642-59448-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41110-9
Online ISBN: 978-3-642-59448-9
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