Fibonacci and Lucas numbers with applications Front Matter 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 Pascals Triangle Pascal Like Triangles Additional Pascal Like Triangles Hosoyas 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 Fundamentals 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 References Solutions to Odd Numbered Exercises Index Pure and Applied Mathematics. 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 Pascals Triangle Pascal Like Triangles Additional Pascal Like Triangles Hosoyas 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.