Applications of Fibonacci numbers : proceedings of 'The Second International Conference on Fibonacci Numbers and Their Applications' San Jose State University, California, U.S.A. August, 1986

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. Front Matter....Pages i-xx Fermat-Like Binomial Equations....Pages 1-5 Recurrences Related to the Bessel Function....Pages 7-16 Symmetric Recursive Sequences Mod M....Pages 17-28 Primitive Divisors of Lucas Numbers....Pages 29-38 A Congruence Relation for a Linear Recursive Sequence of Arbitrary Order....Pages 39-44 Fibonacci Numbers and Groups....Pages 45-60 A Triangular Array with Hexagon Property, Dual to Pascal’s Triangle....Pages 61-67 Functions of the Kronecker Square of the Matrix Q....Pages 69-76 Fibonacci Numbers of the Forms PX 2 ± 1, PX 3 ± 1, Where P is Prime....Pages 77-88 On the K-TH Order Linear Recurrence and Some Probability Applications....Pages 89-96 On the Representation of Integral Sequences {F n /d} and {L n /d} as Sums of Fibonacci Numbers and as Sums of Lucas Numbers....Pages 97-112 Primes Having an Incomplete System of Residues for a Class of Second-Order Recurrences....Pages 113-141 Covering the Integers with Linear Recurrences....Pages 143-147 Recursive Theorems for Success Runs and Reliability of Consecutive-K-Out-of-N: F Systems....Pages 149-161 Asveld’s Polynomials p j (n)....Pages 163-176 More on the Problem of Diophantus....Pages 177-181 On a Problem of Diophantus....Pages 183-191 The Generalized Fibonacci Numbers {C n }, C n = C n-1 + C n-2 + K....Pages 193-205 First Failures....Pages 207-210 Back Matter....Pages 211-217 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.