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This book contains thirty-six papers from among the forty-five papers presented at the Third International Conference on Fibonacci Numbers and Their Applications which was held in Pisa, Italy from July 25 to July 29, 1988 in honor of Leonardo de Pisa. 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 are their unifying bond. It is anticipated that this book, like its two predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. August 1989 The Editors Gerald E. Bergum South Dakota State University Brookings, South Dakota, U. S. A. Andreas N. Philippou Ministry of Education Nicosia, Cyprus Alwyn F. Horadam University of New England Armidale N. S. W. , Australia xv THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Dvornicich, Roberto, Chairman Horadam, A. F. (Australia), Co-chairman Filipponi, Piero Philippou, A. N. (Cyprus), Co-chairman Perelli, Alberto Ando, S. (Japan) Viola, Carlo Bergum, G. E. (U. S. A. ) Zannier, Umberto Johnson, M. B. (U. S. A. ) Kiss, P. (Hungary) Tijdeman, Robert (The Netherlands) Tognetti, K. (Australia) XVII LIST OF CONTRIBUTORS TO THE CONFERENCE' ADLER, I. , RR 1, Box 532, North Bennington, VT 05257-9748. "Separating the Biological from the Mathematical Aspects of Phyllotaxis. " *AKRITAS, A. G. , (coauthor P. G. Bradford). "The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations.








Content:
Front Matter....Pages i-xxiv
The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations....Pages 1-6
A GCD Property on Pascal’s Pyramid and the Corresponding LCM Property of the Modified Pascal Pyramid....Pages 7-14
Translatable and Rotatable Configurations which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously....Pages 15-26
Fibonacci Length of Generating Pairs in Groups....Pages 27-35
A Generalization of Fibonacci Trees....Pages 37-56
Generalized Fibonacci Numbers are Rounded Powers....Pages 57-62
On Generalized Fibonacci Numbers of Graphs....Pages 63-76
An Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles....Pages 77-88
Representation of Natural Numbers as Sums of Fibonacci Numbers: An Application to Modern Cryptography....Pages 89-99
A Note on Ramifications Concerning the Construction of Pythagorean Triples from Recursive Sequences....Pages 101-106
Functional Recurrences....Pages 107-114
Concentric Cycles in Mosaic Graphs....Pages 115-121
Fibonacci Triangles....Pages 123-128
Mosaic Numbers of Fibonacci Trees....Pages 129-132
Falling Factorial Polynomials of Generalized Fibonacci Type....Pages 133-138
Some Notes on Fibonacci Binary Sequences....Pages 139-153
Congruences for Weighted and Degenerate Stirling Numbers....Pages 155-160
An Inverse Theorem on Fibonacci Numbers....Pages 161-170
Some Results on Divisibility Sequences....Pages 171-179
On Mental Calculation of Repeating Decimals, Finding Fibonacci Numbers and a Connection to Pascal’s Triangle....Pages 181-189
Diophantine Representation of Fibonacci Numbers Over Natural Numbers....Pages 191-195
On Prime Divisors of the Terms of Second Order Linear Recurrence Sequences....Pages 197-201
An Alternating Product Representation for Real Numbers....Pages 203-207
Maximum Length of the Euclidean Algorithm and Continued Fractions in F(X)....Pages 209-216
Recurrence Relations in Sinusoids and Their Applications to Spectral Analysis and to the Resolution of Algebraic Equations....Pages 217-222
A Recurrence Relation for Gaussian Multinomial Coefficients....Pages 223-238
Some Binomial Fibonacci Identities....Pages 239-240
A Survey of Properties of Third Order Pell Diagonal Functions....Pages 241-254
Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order....Pages 255-271
Longest Circular Runs with an Application in Reliability Via the Fibonacci-Type Polynomials of Order K....Pages 273-279
Fibonacci Numbers and an Algorithm of Lemoine and K?tai....Pages 281-286
Generalizations of Sequences of Lucas and Bell....Pages 287-297
Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P....Pages 299-309
The Fibonacci Tree, Hofstadter and the Golden String....Pages 311-324
Three Number Trees - Their Growth Rules and Related Number Properties....Pages 325-334
Back Matter....Pages 335-350
....Pages 351-357
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