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Applications of Fibonacci Numbers

Volume 2

  • Book
  • © 1988

Overview

Editors:
  1. A. N. Philippou

    1. Department of Mathematics, University of Patras, Greece

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  2. A. F. Horadam

    1. Department of Mathematics, Statistics and Computer Science, University of New England, Armidale, Australia

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  3. G. E. Bergum

    1. Computer Science Department, South Dakota State University, Brookings, USA

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Fermat-Like Binomial Equations

    • Heiko Harborth
    Pages 1-5

  3. Recurrences Related to the Bessel Function

    • F. T. Howard
    Pages 7-16

  4. Symmetric Recursive Sequences Mod M

    • Kenji Nagasaka, Shiro Ando
    Pages 17-28

  5. Primitive Divisors of Lucas Numbers

    • Peter Kiss
    Pages 29-38

  6. A Congruence Relation for a Linear Recursive Sequence of Arbitrary Order

    • H. T. Freitag, G. M. Phillips
    Pages 39-44

  7. Fibonacci Numbers and Groups

    • Colin M. Campbell, Edmund F. Robertson, Richard M. Thomas
    Pages 45-60

  8. A Triangular Array with Hexagon Property, Dual to Pascal’s Triangle

    • Shiro Ando
    Pages 61-67

  9. Functions of the Kronecker Square of the Matrix Q

    • Odoardo Brugia, Piero Filipponi
    Pages 69-76

  10. Fibonacci Numbers of the Forms PX2 ± 1, PX3 ± 1, Where P is Prime

    • Neville Robbins
    Pages 77-88

  11. On the K-TH Order Linear Recurrence and Some Probability Applications

    • George N. Philippou
    Pages 89-96

  12. On the Representation of Integral Sequences {Fn/d} and {Ln/d} as Sums of Fibonacci Numbers and as Sums of Lucas Numbers

    • Herta T. Freitag, Piero Filipponi
    Pages 97-112

  13. Primes Having an Incomplete System of Residues for a Class of Second-Order Recurrences

    • Lawrence Somer
    Pages 113-141

  14. Covering the Integers with Linear Recurrences

    • John R. Burke, Gerald E. Bergum
    Pages 143-147

  15. Recursive Theorems for Success Runs and Reliability of Consecutive-K-Out-of-N: F Systems

    • Andreas N. Philippou
    Pages 149-161

  16. Asveld’s Polynomials pj(n)

    • A. F. Horadam, A. G. Shannon
    Pages 163-176

  17. More on the Problem of Diophantus

    • Joseph Arkin, Gerald Bergum
    Pages 177-181

  18. On a Problem of Diophantus

    • Calvin Long, Gerald Bergum
    Pages 183-191

  19. The Generalized Fibonacci Numbers {Cn}, Cn = Cn-1 + Cn-2 + K

    • Marjorie Bicknell-Johnson, Gerald E. Bergum
    Pages 193-205

  20. First Failures

    • Dmitri Thoro
    Pages 207-210
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Keywords

About this book

This book contains nineteen papers from among the twenty-five papers presented at the Second International Conference on Fibonacci Numbers and Their Applications. These papers have been selected after a careful review by well known referee's in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers are their unifying bond. It is anticipated that this book will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 1987 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Andreas N. Philippou University of Patras Patras, Greece Alwyn F. Horadam University of New England Armidale, N.S.W., Australia xiii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERN A TIONAL COMMITTEE Bergum, G., Chairman Philippou, A. (Greece), Chairman Edgar, H., Co-chalrman Horadam, A. (Australia), Co-chalrman Bergum, G. (U.s.A.) Thoro, D. Kiss, P. (Hungary) Johnson, M. Long, C. (U.S.A.) Lange, L.

Editors and Affiliations

  • Department of Mathematics, University of Patras, Greece

    A. N. Philippou

  • Department of Mathematics, Statistics and Computer Science, University of New England, Armidale, Australia

    A. F. Horadam

  • Computer Science Department, South Dakota State University, Brookings, USA

    G. E. Bergum

Bibliographic Information

  • Book Title: Applications of Fibonacci Numbers

  • Book Subtitle: Volume 2

  • Editors: A. N. Philippou, A. F. Horadam, G. E. Bergum

  • DOI: https://doi.org/10.1007/978-94-015-7801-1

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media B.V. 1988

  • Hardcover ISBN: 978-90-277-2673-5Published: 30 April 1988

  • Softcover ISBN: 978-90-481-8447-7Published: 30 December 2010

  • eBook ISBN: 978-94-015-7801-1Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: XX, 217

  • Topics: Algebra

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