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Transformations of Fibonacci-Lucas Identities

  • Chapter
Applications of Fibonacci Numbers

Abstract

Fibonacci-Lucas identities (FL-identities) are identities of expressions made up from elements of the Fibonacci and Lucas sequences F n and L n , for example

$$ {F_{{2n}}} = {F_n}{L_n}\;and $$
(1.1)
$$ {L_{{2n}}} = L_n^2 - 2{\left( { - 1} \right)^n}, $$
(1.2)

and such identities are true for all values of the subscript n.

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References

  1. Brooke, M. “Fibonacci Formulas.” The Fibonacci Quarterly, Vol. 1.2 (1963): p. 60.

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  2. Carlitz, L. and Ferns, H.H. “Some Fibonacci and Lucas Identities.” The Fibonacci Quarterly, Vol. 8.1 (1970): pp. 61–73.

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  3. Hilton, A.J.W. “On the Partition of Horadam’s Generalized Sequences into Generalized Fibonacci and Generalized Lucas Sequences.” The Fibonacci Quarterly, Vol. 12.4 (1974): pp. 339–345.

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  4. Hoggatt, V.E. Fibonacci and Lucas Numbers. Houghton Mifflin, Boston, 1969.

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  6. Problem proposed, The Fibonacci Quarterly, Vol. 22.1 (1984): p. 89,

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  7. Partial solution, The Fibonacci Quarterly 27.2 (1989): pp. 188–191

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  8. Partial solution, The Fibonacci Quarterly 28.2 (1990): pp. 187–188.

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  9. Wulczyn, G. “A Generalized Extension of some Fibonacci-Lucas Identities to Primitive Unit Identities.” The Fibonacci Quarterly, Vol. 19.5 (1981): pp. 385–391.

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Authors
  1. L. A. G. Dresel
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Editor information

Editors and Affiliations

  1. Computer Science Department, South Dakota State University, Box 2201, Brookings, South Dakota, 57007-0194, USA

    Gerald E. Bergum

  2. Ministry of Education, Government House Z 50, Nicosia, Cyprus

    Andreas N. Philippou

  3. Department of Mathematics, Statistics and Computer Science, University of New England, Armidale, New South Wales, 2351, Australia

    Alwyn F. Horadam

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© 1993 Springer Science+Business Media Dordrecht

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Dresel, L.A.G. (1993). Transformations of Fibonacci-Lucas Identities. 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_16

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  • DOI: https://doi.org/10.1007/978-94-011-2058-6_16

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4912-2

  • Online ISBN: 978-94-011-2058-6

  • eBook Packages: Springer Book Archive

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