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Divisibility properties of some fibonacci-type sequences

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Book cover Combinatorial Mathematics VI

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 748))

Abstract

A generalized Fibonacci-type sequence is defined from a fourth order homogeneous linear recurrence relation, and various divisibility properties are developed. In particular, the notion of a proper divisor is modified to develop formulas for proper divisors in terms of the general terms of the recurrence sequences and various arithmetic functions.

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References

  1. R. Barakat, "The matrix operator ex and the Lucas polynomials", J. Math. and Physics, 43 (1964), 332–335.

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  2. L. Bernstein, "Explicit solutions of pyramidal Diophantine equations", Canad. Math. Bull., 15 (1972), 177–184.

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  5. A.F. Horadam, "Pell identities", Fibonacci Quart., 9 (1971), 245–252, 263.

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  6. A.G. Shannon, A.F. Horadam and R.P. Loh, "Proper divisors of Lenakel numbers", Math. Stud., (to appear).

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  7. N.N. Vorob'ev, Fibonacci Numbers. (Pergamon, Oxford, 1961.)

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of New England, 2351, Armidale, N.S.W.

    A. F. Horadam, R. P. Loh & A. G. Shannon

  2. Department of Applied Mathematics, University of Sydney, 2006, Sydney, N.S.W.

    A. F. Horadam, R. P. Loh & A. G. Shannon

  3. School of Mathematical Sciences, N.S.W. Institute of Technology, 2007, Broadway, N.S.W.

    A. F. Horadam, R. P. Loh & A. G. Shannon

Authors
  1. A. F. Horadam
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  2. R. P. Loh
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  3. A. G. Shannon
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Editor information

A. F. Horadam W. D. Wallis

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© 1979 Springer-Verlag

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Horadam, A.F., Loh, R.P., Shannon, A.G. (1979). Divisibility properties of some fibonacci-type sequences. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102684

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  • DOI: https://doi.org/10.1007/BFb0102684

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

  • eBook Packages: Springer Book Archive

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