Applications of Fibonacci numbers. : Volume 9 proceedings of the Tenth International research conference on Fibonacci numbers and their applications

A report on the tenth international conference. Authors, coauthors and other conference participants. Foreword. The organizing committees. List of contributors to the conference. Introduction. Fibonacci, Vern and Dan. Universal Bernoulli polynomials and P-adic congruences; A. Adelberg. A generalization of Durrmeyer-type polynomials and their approximation properties; O. Agratini. Fibinomial identities; A.T. Benjamin, J.J. Quinn, J.A. Rouse. Recounting binomial Fibonacci identities; A.T. Benjamin, J.A. Rouse. The Fibonacci diatomic array applied to Fibonacci representations; M. Bicknell-Johnson. Finding Fibonacci in a fractal; N.C. Blecke, K. Fleming, G.W. Grossman. Positive integers (a2 + b2) / (ab + 1) are squares; J.-P. Bode, H. Harborth. On the Fibonacci length of powers of dihedral groups; C.M. Campbell, P.P. Campbell, H. Doostie, E.F. Robertson. Some sums related to sums of Oresme numbers; C.K. Cook. Some thoughts on rook polynomials on square chessboards; D. Fielder. Pythagorean quadrilaterals; R. Hochberg, G. Hurlbert. A general lacunary recurrence formula; F.T. Howard. Ordering words and sets of numbers: the Fibonacci case; C. Kimberling. Some basic properties of a Tribonacci line-sequence; J.Y. Lee. A type of sequence constructed from Fibonacci numbers; Aihua. Li, S. Unnithan. Cullen numbers in binary recurrent sequences; F. Luca, P. Stanica. A generalization of Euler's formula and its connection to Bonacci numbers; J.F. Mason, R.H. Hudson. Extensions of generalized binomial coefficients; R.L. Ollerton, A.G. Shannon. Some parity results regarding t-core partitions; N. Robbins, M.V. Subbarao. Generalized Pell numbers and polynomials; A.G. Shannon, A.F. Horadam. A further note on Lucasian numbers; L. Somer. Some constructions and theorems in Goldpoint geometry; J.C. Turner. Some applications of triangle transformations in Fibonacci geometry; J.C. Turner. Cryptography and Lucas sequence discrete logarithms; W.A. Webb. Divisibility of an F-L type convolution; M. Wiemann, C. Cooper. Generating functions of convolution matrices; Yongzhi (Peter) Yang. F-L representation of division of polynomials over a ring; Chizhong Zhou, F.T. Howard. Subject Index Cover......Page 1 Front matter......Page 2 1. Universal Bernoulli Polynomials and P-Adic Congruences......Page 32 2. A Generalization of Durrmeyer-Type Polynomials and their Approximation Properties......Page 40 3. Fibinomial Identities......Page 50 4. Recounting Binomial Fibonacci Identities......Page 56 5. The Fibonacci Diatomic Array Applied to Fibonacci Representations......Page 60 6. On Purple Parrots, Fibonacci Numbers, and Color Theory......Page 70 7. Finding Fibonacci in a Fractal......Page 74 8. Positive Integers (......Page 94 9. On the Fibonacci Length of Powers of Dihedral Groups......Page 99 10. Some Sums Related to Sums of Oresme Numbers......Page 116 11. Some Thoughts on Rook Polynomials on Square Chessboards......Page 129 12. Pythagorean Quadrilaterals......Page 137 13. A General Lacunary Recurrence Formula......Page 148 14. Ordering Words and Sets of Numbers: The Fibonacci Case......Page 163 15. Some Basic Properties of a Tribonacci Line-Sequence......Page 171 16. A Type of Sequence Constructed from Fibonacci Numbers......Page 184 17. Cullen Numbers in Binary Recurrent Sequences......Page 192 18. A Generalization of Euler’s Formula and its Connection to Fibonacci Numbers......Page 201 19. Extensions of Generalized Binomial Coefficients......Page 210 20. Some Parity Results Regarding......Page 223 21. Generalized Pell Numbers and Polynomials......Page 234 22. A Further Note on Lucasian Numbers......Page 246 23. Some Constructions and Theorems in Goldpoint Geometry......Page 256 24. Some Applications of Triangle Transformations in Fibonacci Geometry......Page 267 25. Cryptography and Lucas Sequence Discrete Logarithms......Page 282 26. Divisibility of an F-L Type Convolution......Page 286 27. Generating Functions of Convolution Matrices......Page 307 28. F-L Representation of Division of Polynomials over a Ring......Page 314 Back matter......Page 326 This Volume Presents The Proceedings Of The Tenth International Conference On Fibonacci Numbers And Their Applications, Held In June 2002 In Flagstaff, Arizona. It Contains Research Papers On The Fibonacci Numbers And Their Generalizations. All Papers Were Carefully Refereed For Content And Originality. The Authors Represent Eight Different Countries. This Volume Will Be Of Interest To Graduate Students And Research Mathematicians, Whose Work Involves Number Theory, Combinatorics, Algebraic Number Theory, Finite Geometry And Special Functions. Edited By Frederic T. Howard. Proceedings of the Tenth International Research Conference on Fibonacci Numbers and Their Applications, held in Flagstaff, Arizona, USA, June 2002 The classical Bernoulli numbers Bn are defined by t/et - 1 = n=0 Bn tn/n!.