# Applications of Fibonacci Numbers : Volume 6 Proceedings of `The Sixth International Research Conference on Fibonacci Numbers and Their Applications', Washington State University, Pullman, Washington, U.S.A., July 18-22, 1994

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This book contains 43 papers form among the 55 papers presented at the Sixth International Conference on Fibonacci Numbers and Their Applications which was held at Washington State University, Pullman, Washington, from July 18-22, 1994. These papers have been selected after a careful review by well known referees in the field, and they range from elementary number theory to probability and statistics. The Fibonacci numbers and recurrence relations are their unifying bond. It is anticipated that this book, like its five predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. October 30, 1995 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U.S.A. Alwyn F. Horadam University of New England Armidale, N.S.W., Australia Andreas N. Philippou 26 Atlantis Street Aglangia, Nicosia Cyprus xxi THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Long, Calvin T., Co-Chair Horadam, A.F. (Australia), Co-Chair Webb, William A., Co-Chair Philippou, A.N. (Cyprus), Co-Chair Burke, John Ando, S. (Japan) DeTemple, Duane W.

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## Product details

- Hardback | 551 pages
- 160 x 240 x 44.45mm | 1,152g
- 01 Mar 1996
- Springer
- Dordrecht, Netherlands
- English
- 1996 ed.
- XXVIII, 551 p.
- 0792339568
- 9780792339564

## Back cover copy

This volume contains the proceedings of the Sixth International Research Conference on Fibonacci Numbers and their Applications. It includes a carefully refereed collection of papers dealing with number patterns, linear recurrences and the application of the Fibonacci Numbers to probability, statistics, differential equations, cryptography, computer science and elementary number theory. This volume provides a platform for recent discoveries and encourages further research. It is a continuation of the work presented in the previously published proceedings of the earlier conferences, and shows the growing interest in, and importance of, the pure and applied aspects of Fibonacci Numbers in many different areas of science. This book will be of interest to those whose work involves number theory, statistics and probability, algebra, numerical analysis, group theory and generalisations.

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## Table of contents

Advances in Linear Pixel Shuffling; P.G. Anderson. Minimal Center Covering Stars with Respect to LCM in Pascal's Pyramid and its Generalizations; S. Ando, D. Sato. Multiple Color Version of the Star of David Theorems on Pascal's Triangle and Related Arrays of Numbers; S. Ando, D. Sato. Some Remarks on the Distribution of Second Order Recurrences and a Related Group Structure; J.R. Burke. Matrices, Recurrent Sequences and Arithmetic; U. Cerruti, F. Vaccarino. Vector Linear Recurrent Sequences in Commutative Rings; U. Cerruti, F. Vaccarino. Subwords of the Golden Sequence and the Fibonacci Words; W.-F. Chuan. Interesting Arrays Associated with Fibonacci Sequences; M.N. Deshpande, G.E. Bergum. More Applications of a Partition Driven Symmetric Table; D.C. Fielder, C.O. Alford. Partial Derivative Sequences of Second-Order Recurrence Polynomials; P. Filipponi, A.F. Horadam. The Zeckendorf Decomposition of Certain Classes of Integers; P. Filipponi, H.T. Freitag. On the Sum of Consecutive Squares; H.T. Freitag, G.M. Phillips. Rado Numbers of Fibonacci Sequences and a Problem of S. Rabinowitz; H. Harborth, S. Maasberg. Rooks on Fibonacci Boards; H. Harborth, L. Piepmeyer. Tiling with Cuisenaire Rods; E. Hare, P. Chinn. Hofstadter's Conjecture for alphaSQRT2 - 1; R.J. Hendel. Recursive Properties of Trigonometric Products; R.J. Hendel, C.K. Cook. A Synthesis of Certain Polynomial Sequences; A.F. Horadam. On Dichotomous Complexity of the Fibonacci Tree; Y. Horibe. Formulas of Ramanujan Involving Lucas Numbers, Pell Numbers, and Bernoulli Numbers; F.T. Howard. Counting Sets of Integers with Various Summation Properties; D. Jennings. Factorial and Binomial Coefficients in Polynomial Rings over Finite Fields; W.A. Kimball. An Identify Involving the q-Factorial; Z.F. Kocak, G.M. Phillips. GCD Properties of an Octagon; E. Korntved. Products and Quotients of Difference Equations; J. Lahr. The Wythoff and the Zeckendorf Representations of Numbers are Equivalent; W. Lang. Some Basic Translational Properties of the General Fibonacci Line-Sequence; J.Y. Lee. Pentagonal Numbers in Fibonacci Sequence; M. Luo. On Reciprocal Sums of Second Order Sequences; R.S. Melham, A.G. Shannon. Solving Linear Recurrences from Differential Equations in the Exponential Manner and Vice Versa; W. Oberschelp. The Rational Heart of Integer Fibonacci Pentagons; B.E. Peterson, J.H. Jordan. Algorithmic Manipulation of Fibonacci Identities; S. Rabinowitz. On Lucas Pseudoprimes of the Form ax2 + bxy + cy2; A. Rotkiewicz. On Certain Rational Expressions whose Prime Divisors are Cubic Residues (Mod P); K.-I. Sato, S. Shirai. A Search for Solutions of a Functional Equation; A.G. Shannon, et al. A Use of Generalized Fibonacci Numbers in Finding Quadratic Factors; A.G. Shannon, et al. Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P-III; L. Somer. Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts; L. Somer. On a Model of the Modular Group; J.C. Turner, A.G. Schaake. Properties of a k-Order Linear Recursive Sequence Modulo m; M.E. Waddill. Residue Counts Modulo Three for the Fibonacci Triangle; D.L. Wells. On a Class of Congruences for Lucas Sequences; P.T. Young. Subject Index.

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