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k-Fibonacci sequences modulo m

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  • Falcon, Sergio
  • Plaza, Ángel

Abstract

We study here the period-length of the k-Fibonacci sequences taken modulo m. The period of such cyclic sequences is know as Pisano period, and the period-length is denoted by πk(m). It is proved that for every odd number k, πk(k2+4)=4(k2+4).

Suggested Citation

  • Falcon, Sergio & Plaza, Ángel, 2009. "k-Fibonacci sequences modulo m," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 497-504.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:497-504
    DOI: 10.1016/j.chaos.2008.02.014
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    References listed on IDEAS

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    1. Stakhov, Alexey, 2007. "The generalized golden proportions, a new theory of real numbers, and ternary mirror-symmetrical arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 315-334.
    2. El Naschie, M.S., 2005. "Non-Euclidean spacetime structure and the two-slit experiment," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 1-6.
    3. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
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    5. El Naschie, M.S., 2005. "Stability Analysis of the two-slit experiment with quantum particles," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 291-294.
    6. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    7. Stakhov, A.P., 2005. "The Generalized Principle of the Golden Section and its applications in mathematics, science, and engineering," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 263-289.
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    Cited by:

    1. Deveci, Ömür & Hulku, Sakine & Shannon, Anthony G., 2021. "On the co-complex-type k-Fibonacci numbers," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).

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