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Properties of a k-Order Linear Recursive Sequence Modulo m

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Applications of Fibonacci Numbers
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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].

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References

  1. Andressian, Agnes “Fibonacci Sequences Modulo M”. The Fibonacci Quarterly, Vol. 12.1 (1974): pp. 51–64.

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  2. Chang, Derek K. “Higher-Ordered Fibonacci Sequences Modulo m”. The Fibonacci Quarterly, Vol. 24.2 (1986): pp. 138–139.

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  3. Dresel, L.A.G. “Letter to the Editor”. The Fibonacci Quarterly, Vol. 15.4 (1977): p. 346.

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  4. Halton, John H. “On the Divisibility Properties of the Fibonacci Numbers”. The Fibonacci Quarterly, Vol. 4.3 (1966): pp. 217–239.

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  5. Penney, David E. and Pomerance, Carl. “Solution to Problem 2539”. The American Mathematical Monthly, Vol. 83.9 (1976): pp. 742–743.

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  6. Vince, Andrew. “The Fibonacci Sequence Modulo N”. The Fibonacci Quarterly, Vol. 16.5, (1978): pp. 403–407.

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  7. Vince, Andrew. “Period of a Linear Recurrence”. Acta Arithmetical, Vol. 39.4 (1981): pp. 303–311.

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  8. Waddill, Marcellus E. “Some Properties of a Generalized Fibonacci Sequence Modulo m.” The Fibonacci Quarterly, Vol. 164 (1978): pp. 344–353.

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  9. Waddill, Marcellus E. “Some Properties of the Tetranacci Sequence Modulo m.” The Fibonacci Quarterly, Vol. 30.3 (1992): pp. 232–238.

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  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.

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  11. Wall, D.D. “Fibonacci Series Modulo m.” The American Mathematical Monthly, Vol. 67.6, (1960): pp. 525–532.

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© 1996 Kluwer Academic Publishers

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Waddill, M.E. (1996). Properties of a k-Order Linear Recursive Sequence Modulo m. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0223-7_41

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  • DOI: https://doi.org/10.1007/978-94-009-0223-7_41

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6583-2

  • Online ISBN: 978-94-009-0223-7

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