Ebook: 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

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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This volume contains the proceedings of the Sixth International Research Conference on Fibonacci Numbers and their Applications. It includes a carefully refereed selection of papers dealing with number patterns, linear recurrences and the application of 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.
Audience: This book will be of interest to those whose work involves number theory, statistics and probability, numerical analysis, group theory and generalisations.

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This volume contains the proceedings of the Sixth International Research Conference on Fibonacci Numbers and their Applications. It includes a carefully refereed selection of papers dealing with number patterns, linear recurrences and the application of 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.
Audience: This book will be of interest to those whose work involves number theory, statistics and probability, numerical analysis, group theory and generalisations.
Content:
Front Matter....Pages i-xxviii
Advances in Linear Pixel Shuffling....Pages 1-21
Minimal Center Covering Stars with Respect to LCM in Pascal’s Pyramid and its Generalizations....Pages 23-30
Multiple Color Version of the Star of David Theorems on Pascal’s Triangle and Related Arrays of Numbers....Pages 31-45
Some Remarks on the Distribution of Second Order Recurrences and a Related Group Structure....Pages 47-52
Matrices, Recurrent Sequences and Arithmetic....Pages 53-62
Vector Linear Recurrence Sequences in Commutative Rings....Pages 63-72
Subwords of the Golden Sequence and the Fibonacci Words....Pages 73-84
Interesting Arrays Associated with Fibonacci Sequences....Pages 85-92
More Applications of a Partition Driven Symmetric Table....Pages 93-103
Partial Derivative Sequences of Second-Order Recurrence Polynomials....Pages 105-122
The Zeckendorf Decomposition of Certain Classes of Integers....Pages 123-135
On the Sum of Consecutive Squares....Pages 137-142
Rado Numbers for Fibonacci Sequences and a Problem of S. Rabinowitz....Pages 143-153
Rooks on Fibonacci Boards....Pages 155-163
Tiling with Cuisenaire Rods....Pages 165-171
Recursive Properties of Trigonometric Products....Pages 173-199
A Synthesis of Certain Polynomial Sequences....Pages 201-214
Minmax Sequences for Pell Numbers....Pages 215-229
On Dichotomous Complexity of the Fibonacci Tree....Pages 231-249
Formulas of Ramanujan Involving Lucas Numbers, Pell Numbers, and Bernoulli Numbers....Pages 251-256
Counting Sets of Integers with Various Summation Properties....Pages 257-270
Factorials & Binomial Coefficients in Polynomial Rings Over Finite Fields....Pages 271-281
An Identity Involving the q-Factorial....Pages 283-290
GCD Properties of an Octagon....Pages 291-296
Products and Quotients of Difference Equations....Pages 297-302
The Wythoff and the Zeckendorf Representations of Numbers are Equivalent....Pages 303-320
Some Basic Translational Properties of the General Fibonacci Line-Sequence....Pages 321-337
Pentagonal Numbers in the Fibonacci Sequence....Pages 339-347
On Reciprocal Sums of Second Order Sequences....Pages 349-354
Solving Linear Recurrences from Differential Equations in the Exponential Manner and Vice Versa....Pages 355-364
The Rational Heart of the Integer Fibonacci Pentagons....Pages 365-380
Algorithmic Manipulation of Fibonacci Identities....Pages 381-388
N Certain Rational Expressions whose Prime Divisors are Cubic Residues (Mod P)....Pages 389-408
A Search for Solutions of a Functional Equation....Pages 409-421
A Use of Generalized Fibonacci Numbers in Finding Quadratic Factors....Pages 423-429
Distribution of Residues of Certain Second-Order Linear Recurrences Modulo p-III....Pages 431-441
Divisibility of Terms in Lucas Sequences of the Second Kind by Their Subscripts....Pages 443-450
On a Model of the Modular Group....Pages 451-471
Properties of a k-Order Linear Recursive Sequence Modulo m....Pages 473-486
Residue Counts Modulo Three for the Fibonacci Triangle....Pages 487-504
On a Class of Congruences for Lucas Sequences....Pages 505-519
Back Matter....Pages 521-536
....Pages 537-544