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On the Rank of Appearance of Lucas Sequences

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Applications of Fibonacci Numbers

Abstract

Motivated by the study of the order of a group element and its importance for (cryptographic) applications we suggest a generalization of the order-concept in terms of the rank of appearance for Lucas sequences. After summarizing some important properties of the rank of appearance, we give a short description and portray some relationships to similar concepts involving the periodicity of linear recurrences. The goal of this paper is to establish the number of parameters with the same rank of appearance modulo a prime p. To this end, special cases in varying and counting the parameters will be considered.

Research supported by the Österreichischen Fonds zur Förderung der wissenschaftlichen Forschung, FWF-Project no. P 13088-MAT.

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Authors
  1. Siguna Müller
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Editors and Affiliations

  1. Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, North Carolina, USA

    Fredric T. Howard

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© 1999 Springer Science+Business Media Dordrecht

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Müller, S. (1999). On the Rank of Appearance of Lucas Sequences. In: Howard, F.T. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4271-7_26

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  • DOI: https://doi.org/10.1007/978-94-011-4271-7_26

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5851-3

  • Online ISBN: 978-94-011-4271-7

  • eBook Packages: Springer Book Archive

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