Properties of a k-Order Linear Recursive Sequence Modulo m

  • Marcellus E. Waddill

Abstract

Since Wall’s paper [11] first appeared in 1960, a number of scholars have considered various generalizations of the Fibonacci Sequence modulo m. See, for example, [1], [2], [4], [6], [8], [9].

Keywords

Induction Hypothesis Fibonacci Sequence Induction Proof Linear Recurrence Matrix Technique 
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]
    Andressian, Agnes “Fibonacci Sequences Modulo M”. The Fibonacci Quarterly, Vol. 12.1 (1974): pp. 51–64. MathSciNetGoogle Scholar
  2. [2]
    Chang, Derek K. “Higher-Ordered Fibonacci Sequences Modulo m”. The Fibonacci Quarterly, Vol. 24.2 (1986): pp. 138–139. MathSciNetMATHGoogle Scholar
  3. [3]
    Dresel, L.A.G. “Letter to the Editor”. The Fibonacci Quarterly, Vol. 15.4 (1977): p. 346. Google Scholar
  4. [4]
    Halton, John H. “On the Divisibility Properties of the Fibonacci Numbers”. The Fibonacci Quarterly, Vol. 4.3 (1966): pp. 217–239. MathSciNetMATHGoogle Scholar
  5. [5]
    Penney, David E. and Pomerance, Carl. “Solution to Problem 2539”. The American Mathematical Monthly, Vol. 83.9 (1976): pp. 742–743. MathSciNetCrossRefGoogle Scholar
  6. [6]
    Vince, Andrew. “The Fibonacci Sequence Modulo N”. The Fibonacci Quarterly, Vol. 16.5, (1978): pp. 403–407. MathSciNetMATHGoogle Scholar
  7. [7]
    Vince, Andrew. “Period of a Linear Recurrence”. Acta Arithmetical, Vol. 39.4 (1981): pp. 303–311.MathSciNetMATHGoogle Scholar
  8. [8]
    Waddill, Marcellus E. “Some Properties of a Generalized Fibonacci Sequence Modulo m.” The Fibonacci Quarterly, Vol. 164 (1978): pp. 344–353. MathSciNetGoogle Scholar
  9. [9]
    Waddill, Marcellus E. “Some Properties of the Tetranacci Sequence Modulo m.” The Fibonacci Quarterly, Vol. 30.3 (1992): pp. 232–238. MathSciNetMATHGoogle Scholar
  10. [10]
    Waddill, Marcellus E. “Using Matrix Techniques to Establish Properties of k-order Linear Recursive Sequences.” Applications of Fibonacci Numbers, Vol. 5. Edited by G.E. Bergum, A.N. Philippou and A.F. Horadam, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, pp. 601–615. CrossRefGoogle Scholar
  11. [11]
    Wall, D.D. “Fibonacci Series Modulo m.” The American Mathematical Monthly, Vol. 67.6, (1960): pp. 525–532. MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Marcellus E. Waddill

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