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Applications of Fibonacci Numbers


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Table of Contents

Higher 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. Moeller. 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. Pethoe. 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 Mikolas' 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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