Applications of Fibonacci Numbers

Table of Contents

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   Book Overview
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   Chapter 1 The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations
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   Chapter 2 A GCD Property on Pascal’s Pyramid and the Corresponding LCM Property of the Modified Pascal Pyramid
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   Chapter 3 Translatable and Rotatable Configurations which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously
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   Chapter 4 Fibonacci Length of Generating Pairs in Groups
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   Chapter 5 A Generalization of Fibonacci Trees
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   Chapter 6 Generalized Fibonacci Numbers are Rounded Powers
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   Chapter 7 On Generalized Fibonacci Numbers of Graphs
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   Chapter 8 An Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles
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    Chapter 9 Representation of Natural Numbers as Sums of Fibonacci Numbers: An Application to Modern Cryptography
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    Chapter 10 A Note on Ramifications Concerning the Construction of Pythagorean Triples from Recursive Sequences
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    Chapter 11 On the Representation of {F kn /F n }, {F kn /L n }, {L kn /L n }, and {L kn /F n } as Zeckendorf Sums
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    Chapter 12 Functional Recurrences
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    Chapter 13 Concentric Cycles in Mosaic Graphs
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    Chapter 14 Fibonacci Triangles
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    Chapter 15 Mosaic Numbers of Fibonacci Trees
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    Chapter 16 Falling Factorial Polynomials of Generalized Fibonacci Type
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    Chapter 17 Some Notes on Fibonacci Binary Sequences
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    Chapter 18 Congruences for Weighted and Degenerate Stirling Numbers
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    Chapter 19 An Inverse Theorem on Fibonacci Numbers
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    Chapter 20 Some Results on Divisibility Sequences
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    Chapter 21 On Mental Calculation of Repeating Decimals, Finding Fibonacci Numbers and a Connection to Pascal’s Triangle
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    Chapter 22 Diophantine Representation of Fibonacci Numbers Over Natural Numbers
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    Chapter 23 On Prime Divisors of the Terms of Second Order Linear Recurrence Sequences
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    Chapter 24 An Alternating Product Representation for Real Numbers
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    Chapter 25 Maximum Length of the Euclidean Algorithm and Continued Fractions in F (X)
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    Chapter 26 Recurrence Relations in Sinusoids and Their Applications to Spectral Analysis and to the Resolution of Algebraic Equations
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    Chapter 27 A Recurrence Relation for Gaussian Multinomial Coefficients
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    Chapter 28 Some Binomial Fibonacci Identities
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    Chapter 29 A Survey of Properties of Third Order Pell Diagonal Functions
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    Chapter 30 Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order
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    Chapter 31 Longest Circular Runs with an Application in Reliability Via the Fibonacci-Type Polynomials of Order K
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    Chapter 32 Fibonacci Numbers and an Algorithm of Lemoine and Kátai
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    Chapter 33 Generalizations of Sequences of Lucas and Bell
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    Chapter 34 Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P
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    Chapter 35 The Fibonacci Tree, Hofstadter and the Golden String
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    Chapter 36 Three Number Trees - Their Growth Rules and Related Number Properties