On a Class of Congruences for Lucas Sequences

  • Paul Thomas Young

Abstract

Let ⋋,µ∈ℤ and define a sequence of integers {Hn(λ,μ)}n≥0 by the linear recurrence
$$ {H_0}\left( {\lambda ,\mu } \right) = 2,{H_1}\left( {\lambda ,\mu } \right) = \lambda ,and{H_{n + 1}}\left( {\lambda ,\mu } \right) = \lambda {H_n}\left( {\lambda ,\mu } \right) + \mu {H_{n - 1}}\left( {\lambda ,\mu } \right)forn > 0. $$
(1.1)

Keywords

Distinct Element Algebraic Integer Linear Recurrence Galois Ring Multiplicative Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    André-Jeannin, R. “On a Conjecture of Piero Filipponi”. The Fibonacci Quarterly, Vol. 32.1 (1994): pp. 11–14.Google Scholar
  2. [2]
    Filipponi, P. “A Note on a Class of Lucas Sequences”. The Fibonacci Quarterly, Vol. 29.3 (1991): pp. 256–263.MathSciNetGoogle Scholar
  3. [3]
    Koblitz, N. “p-adic Numbers, p-adic Analysis, and Zeta-functions”. Springer-Verlag, New York, 1977.MATHGoogle Scholar
  4. [4]
    Young, P.T. “p-adic Congruences for Generalized Fibonacci Sequences”. The Fibonacci Quarterly, Vol. 32.1 (1994): pp. 2–10.Google Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Paul Thomas Young

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