Properties of a k-Order Linear Recursive Sequence Modulo m

  • Marcellus E. Waddill


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].


Induction Hypothesis Fibonacci Sequence Induction Proof Linear Recurrence Matrix Technique 
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    Andressian, Agnes “Fibonacci Sequences Modulo M”. The Fibonacci Quarterly, Vol. 12.1 (1974): pp. 51–64. MathSciNetGoogle Scholar
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    Chang, Derek K. “Higher-Ordered Fibonacci Sequences Modulo m”. The Fibonacci Quarterly, Vol. 24.2 (1986): pp. 138–139. MathSciNetzbMATHGoogle Scholar
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    Dresel, L.A.G. “Letter to the Editor”. The Fibonacci Quarterly, Vol. 15.4 (1977): p. 346. Google Scholar
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    Halton, John H. “On the Divisibility Properties of the Fibonacci Numbers”. The Fibonacci Quarterly, Vol. 4.3 (1966): pp. 217–239. MathSciNetzbMATHGoogle Scholar
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    Penney, David E. and Pomerance, Carl. “Solution to Problem 2539”. The American Mathematical Monthly, Vol. 83.9 (1976): pp. 742–743. MathSciNetCrossRefGoogle Scholar
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    Vince, Andrew. “The Fibonacci Sequence Modulo N”. The Fibonacci Quarterly, Vol. 16.5, (1978): pp. 403–407. MathSciNetzbMATHGoogle Scholar
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    Vince, Andrew. “Period of a Linear Recurrence”. Acta Arithmetical, Vol. 39.4 (1981): pp. 303–311.MathSciNetzbMATHGoogle Scholar
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    Waddill, Marcellus E. “Some Properties of a Generalized Fibonacci Sequence Modulo m.” The Fibonacci Quarterly, Vol. 164 (1978): pp. 344–353. MathSciNetGoogle Scholar
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    Waddill, Marcellus E. “Some Properties of the Tetranacci Sequence Modulo m.” The Fibonacci Quarterly, Vol. 30.3 (1992): pp. 232–238. MathSciNetzbMATHGoogle Scholar
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    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
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    Wall, D.D. “Fibonacci Series Modulo m.” The American Mathematical Monthly, Vol. 67.6, (1960): pp. 525–532. MathSciNetzbMATHCrossRefGoogle Scholar

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© Kluwer Academic Publishers 1996

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  • Marcellus E. Waddill

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