Applications of Fibonacci Numbers

Table of Contents

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   Book Overview
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   Chapter 1 A Fibonacci-Based Pseudo-Random Number Generator
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   Chapter 2 On the Proof of GCD and LCM Equalities Concerning the Generalized Binomial and Multinomial Coefficients
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   Chapter 3 Supercube
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   Chapter 4 A Note on Fundamental Properties of Recurring Series
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   Chapter 5 Period Patterns of Certain Second-Order Linear Recurrences Modulo a Prime
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   Chapter 6 Nearly Isosceles Triangles Where the Vertex Angle is a Multiple of the Base Angle
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   Chapter 7 The Ring of Fibonacci (Fibonacci “Numbers” with Matrix Subscript)
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   Chapter 8 One-Relator Products of Cyclic Groups and Fibonacci-Like Sequences
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    Chapter 9 A Generalization of the Fibonacci Search
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    Chapter 10 Pascal’s Triangle: Top Gun or Just One of the Gang?
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    Chapter 11 Conversion of Fibonacci Identities into Hyperbolic Identities Valid for an Arbitrary Argument
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    Chapter 12 Derivative Sequences of Fibonacci and Lucas Polynomials
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    Chapter 13 A Carry Theorem for Rational Binomial Coefficients
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    Chapter 14 On Co-Related Sequences Involving Generalized Fibonacci Numbers
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    Chapter 15 Fibonacci and B-Adic Trees in Mosaic Graphs
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    Chapter 16 Fibonacci Representations of Graphs
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    Chapter 17 On the Sizes of Elements in the Complement of a Submonoid of Integers
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    Chapter 18 Genocchi Polynomials
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    Chapter 19 An Application of Zeckendorf’s Theorem
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    Chapter 20 A New Kind of Golden Triangle
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    Chapter 21 Terms Common to Two Sequences Satisfying the Same Linear Recurrence
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    Chapter 22 Recurrence Relations in Exponential Functions and in Damped Sinusoids and Their Applications in Electronics
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    Chapter 23 Some Basic Properties of the Fibonacci Line-Sequence
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    Chapter 24 De Moivre-Type Identities for the Tetrabonacci Numbers
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    Chapter 25 Two Generalizations of Gould’s Star of David Theorem
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    Chapter 26 On Triangular Lucas Numbers
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    Chapter 27 A Fast Algorithm of the Chinese Remainder Theorem and ITS Application to Fibonacci Numbers
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    Chapter 28 Generating the Pythagorean Triples Via Simple Continued Fractions
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    Chapter 29 On the Moebius Knot Tree and Euclid’s Algorithm
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    Chapter 30 Generalized Fibonacci and Lucas Factorizations
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    Chapter 31 On Even Fibonacci Pseudoprimes
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    Chapter 32 Possible Restricted Periods of Certain Lucas Sequences Modulo P
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    Chapter 33 Using Matrix Techniques to Establish Properties of a Generalized Tribonacci Sequence