Applications of Fibonacci Numbers

1. Front Matter

   Pages i-xx

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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

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.

• binomial
• field
• matrix
• number theory
• prime number

• 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

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