Fibonacci and Lucas numbers with applications / Thomas Koshy.

"A Wiley-Interscience publication."

Includes bibliographical references (pages 562-576) and index.

Leonardo Fibonacci -- The Rabbit Problem -- Fibonacci Numbers in Nature -- Fibonacci Numbers: Additional Occurrences -- Fibonacci and Lucas Identities -- Geometric Paradoxes -- Generalized Fibonacci Numbers -- Additional Fibonacci and Lucas Formulas -- The Euclidean Algorithm -- Solving Recurrence Relations -- Completeness Theorems -- Pascal's Triangle -- Pascal-Like Triangles -- Additional Pascal-Like Triangles -- Hosoya's Triangle -- Divisibility Properties -- Generalized Fibonacci Numbers Revisited -- Generating Functions -- Generating Functions Revisited -- The Golden Ratio -- The Golden Ratio Revisited -- Golden Triangles -- Golden Rectangles -- Fibonacci Geometry -- Regular Pentagons -- The Golden Ellipse and Hyperbola -- Continued Fractions -- Weighted Fibonacci and Lucas Sums -- Fibonacci and Lucas Sums Revisited -- The Knapsack Problem -- Fibonacci Magic Squares -- Fibonacci Matrices -- Fibonacci Determinants -- Fibonacci and Lucas Congruences -- Fibonacci and Lucas Periodicity -- Fibonacci and Lucas Series -- Fibonacci Polynomials -- Lucas Polynomials -- Jacobsthal Polynomials -- Zeros of Fibonacci and Lucas Polynomials -- Morgan-Voyce Polynomials -- Fibonometry -- Fibonacci and Lucas Subscripts -- Gaussian Fibonacci and Lucas Numbers -- Analytic Extensions -- Tribonacci Numbers -- Tribonacci Polynomials -- The First 100 Fibonacci and Lucas Numbers -- The First 100 Fibonacci Numbers and Their Prime Factorizations -- The First 100 Lucas Numbers and Their Prime Factorizations.

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