This book contains 50 papers from among the 95 papers presented at the Seventh International Conference on Fibonacci Numbers and Their Applications which was held at the Institut Fiir Mathematik, Technische Universitiit Graz, Steyrergasse 30, A-SOlO Graz, Austria, from July 15 to July 19, 1996. 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 six predecessors, will be useful to research workers and graduate students interested in the Fibonacci numbers and their applications. September 1, 1997 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 House of Representatives Nicosia, Cyprus xxvii THE ORGANIZING COMMITTEES LOCAL COMMITTEE INTERNATIONAL COMMITTEE Tichy, Robert, Chairman Horadam, A. F. (Australia), Co-Chair Prodinger, Helmut, Co-Chairman Philippou, A. N. (Cyprus), Co-Chair Grabner, Peter Bergurt:t, G. E. (U. S. A. ) Kirschenhofer, Peter Filipponi, P. (Italy) Harborth, H. (Germany) Horibe, Y. (Japan) Johnson, M. (U. S. A. ) Kiss, P. (Hungary) Phillips, G. M. (Scotland) Turner, J. (New Zealand) Waddill, M. E. (U. S. A. ) xxix LIST OF CONTRIBUTORS TO THE CONFERENCE *ADELBERG, ARNOLD, "Higher Order Bernoulli Polynomials and Newton Polygons. " AMMANN, ANDRE, "Associated Fibonacci Sequences. " *ANDERSON, PETER G., "The Fibonacci Shuffle Tree.

InhaltsangabeHigher Order Bernoulli Polynomials and Newton Polygons; A. Adelberg. The Fibonacci Shuffle Tree; P.G. Anderson. On the Period of Sequences Modulo a Prime Satisfying a Second Order Recurrence; S. Ando. Generalizations to Large Hexagons of the Star of David Theorem with Respect to GCD; S. Ando, et al. Longest Success and Failure Runs and New Polynomials Related to the Fibonacci-Type Polynomials of Order K; D.L. Antzoulakos, A.N. Philippou. A Note on a Representation Conjecture by Hoggatt; M. Bicknell-Johnson. Some Remarks on the Distribution of Subsequences of Second Order Linear Recurrences; J.R. Burke. A Criterion for Stability of Two-Term Recurrence Sequences Modulo Odd Primes; W. Carlip, et al. A Problem of Diophantus and Pell Numbers; A. Dujella. On the Exceptional Set in the Problem of Diophantus and Davenport; A. Dujella. Substitutive Numeration Systems and a Combinatorial Problem; J.-M. Dumont. A Note on Derived Linear Recurring Sequences; M. Elia. Observations from Computer Experiments on an Integer Equation; D.C. Fielder, C.O. Alford. Some Probabilistic Aspects of the Zeckendorf Decomposition of Integers; P. Filipponi, H.T. Freitag. First Derivative Sequences of Extended Fibonacci and Lucas Polynomials; P. Filipponi, A.F. Horadam. Elements of Zeckendorf Arithmetic; H.T. Freitag, G.M. Phillips. Binomial Coefficients Generalized with Respect to a Discrete Valuation; S. Frisch. The Dying Fibonacci Tree; B. Gittenberger. Smallest Integral Combinatorial Box; H. Harborth, M. Möller. New Aspects of Morgan-Voyce Polynomials; A.F. Horadam. Growing a Self-Similar Tree; Y. Horibe. Lacunary Sums of Binomial Coefficients; F.T. Howard, R. Witt. Some Reciprocal Summation Identities with Applications to the Fibonacci and LucasNumbers; D. Jennings. A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients; C. Kimberling. On Sums of the Reciprocals of Prime Divisors of Terms of a Linear Recurrence; P. Kiss. A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal; W. Lang. A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature; T.N. Langtry. The Fibonacci Pyramid; T.G. Lavers. On a Three Dimensional Approximation Problem; K. Liptai. Analysis of the Euclidean and Related Algorithms; C.T. Long, W.A. Webb. Fundamental Solutions of u2-5v2 = -4r2; C.T. Long, W.A. Webb. Probable Prime Tests Using Lucas Sequences; W. More. On a Functional Equation Associated with the Fibonacci Numbers; K. Ozeki. Diophantine Properties of Linear Recursive Sequences I; A. Pethö. The Cantor-Fibonacci Distribution; H. Prodinger. On the Parity of Certain Partition Functions; N. Robbins. There are Infinitely Many Arithmetical Progressions Formed by Three Different Fibonacci Pseudoprimes; A. Rotkiewicz. On Mikolás' Summation Formula Involving Farey Fractions; K. Sato. Second Order Linear Recurring Sequences in Hypercomplex Numbers; K. Scheicher. The Bell Differential Polynomials; R. Schimming, S.Z. Rida. On Lucas d-Pseudoprimes; L. Somer. Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal Vs Immortal Trees; C.P. Spears, M. Bicknell-Johnson. The Golden Section and Modern Harmony Mathematics; A.P. Stakhov. Lucas Factors and a Fibonomial Generating Function; I. Strazdins. Elementary Properties of Canonical Number Systems in Quadratic Fields; J.M. Thuswaldner. Three Examples of Tri

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