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A Further Note on Lucasian Numbers

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Applications of Fibonacci Numbers

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Abstract

This paper will extend and unify the results in [4] by completely determining all Lucasian numbers which are terms in certain Lucas sequences. Our specification of all Lucasian numbers will be based on results obtained in [1] in which all terms in particular Lucas sequences which do not have any primitive prime divisors are found.

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References

  1. Bilu, Yu, Hanrot, G. and Voutier, P.M. “Existence of Primitive Divisors of Lucas and Lehmer Numbers.” J. Reine Angew. Math., Vol. 539 (2001): pp. 75–122.

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  4. Hilton, P., Pedersen, J. and Somer, L. “On Lucasian Numbers.” The Fibonacci Quarterly, Vol. 35.1 (1997) : pp. 43–47.

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  7. Somer, L. “Divisibility of Terms in Lucas Sequences of the Second Kind by their Subscripts.” Applications of Fibonacci Numbers. Volume 6. Edited by G.E. Bergum, A.N. Philippou, and A.F. Horadam. Dordrecht; Kluwer (1996), pp. 473–486.

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  8. Somer, L. Solution to Problem B-825 Proposed by L. Somer. The Fibonacci Quarterly, Vol. 35.4 (1997) : p. 376.

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Authors
  1. Lawrence Somer
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Editor information

Editors and Affiliations

  1. Wake Forest University, Winston-Salem, North Carolina, USA

    Frederic T. Howard

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© 2004 Springer Science+Business Media Dordrecht

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Somer, L. (2004). A Further Note on Lucasian Numbers. In: Howard, F.T. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-0-306-48517-6_22

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  • DOI: https://doi.org/10.1007/978-0-306-48517-6_22

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6545-2

  • Online ISBN: 978-0-306-48517-6

  • eBook Packages: Springer Book Archive

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