Applications of Fibonacci Numbers

Higher Order Bernoulli Polynomials and Newton Polygons.- The Fibonacci Shuffle Tree.- On The Period of Sequences Modulo a Prime Satisfying a Second Order Recurrence.- Generalizations to Large Hexagons of The Star of David Theorem With Respect to God.- Longest Success and Failure Runs and New Polynomials Related to The Fibonacci-Type Polynomials of Order K.- A Note on A Representation Conjecture By Hoggatt.- Some Remarks on The Distribution of Subsequences of Second Order Linear Recurrences.- A Criterion for Stability of Two-Term Recurrence Sequences Modulo Odd Primes.- A Problem of Diophantus and Pell Numbers.- On The Exceptional Set in The Problem of Diophantus and Davenport.- Substitutive Numeration Systems and A Combinatorial Problem.- A Note on Derived Linear Recurring Sequences.- Observations from Computer Experiments on an Integer Equation.- Some Probabilistic Aspects of The Zeckendorf Decomposition of Integers.- First Derivative Sequences of Extended Fibonacci and Lucas Polynomials.- Elements of Zeckendorf Arithmetic.- Binomial Coefficients Generalized With Respect to A Discrete Valuation.- The Dying Fibonacci Tree.- Smallest Integral Combinatorial Box.- New Aspects of Morgan-Voyce Polynomials.- Growing A Self-Similar Tree.- Lacunary Sums of Binomial Coefficients.- Some Reciprocal Summation Identities with Applications to The Fibonacci And Lucas Numbers.- A Relative Rank Function on Sets of Continued Fractions Having Bounded Partial Quotients.- On Sums of The Reciprocals of Prime Divisors of Terms of a Linear Recurrence.- A Fibonacci-Fractal: A Bicolored Self-Similar Multifractal.- A Generalisation of Ratios of Fibonacci Numbers with Application to Numerical Quadrature.- The Fibonacci Pyramid.- On A Three Dimensional Approximation Problem.- Analysis of The Euclidean and Related Algorithms.- Fundamental Solutions of u2 — 5v2 = — 4r2.- Probable Prime Tests Using Lucas Sequences.- On a Functional Equation Associated with The Fibonacci Numbers.- Diophantine Properties of Linear Recursive Sequences I.- The Cantor-Fibonacci Distribution.- On The Parity of Certain Partition Functions.- There Are Infinitely Many Arithmetical Progressions Formed By Three Different Fibonacci Pseudoprimes.- On Mikolas’ Summation Formula Involving Farey Fractions.- Second order Linear Recurring Sequences in Hypercomplex Numbers.- The Bell Differential Polynomials.- On Lucas d-Pseudoprimes.- Asymmetric Cell Division: Binomial Identities for Age Analysis of Mortal Vs Immortal Trees.- The Golden Section and Modern Harmony Mathematics.- Lucas Factors and A Fibonomial Generating Function.- Elementary Properties of Canonical Number Systems in Quadratic Fields.- Three Examples of Triangular Arrays with Optimal Discrepancy and Linear Recurrences.- A Multivariate Inverse Polya Distribution Of Order K Arising in the Case Of Overlapping Success Runs.- to A Fibonacci Geometry.- Taylor Functionals and The Solution of Linear Difference Equations.- Section — Invariant Numbers and Generalised Golden Section Optimization Algorithms.