دانلود کتاب Applications of Fibonacci Numbers: Volume 3 Proceedings of ‘The Third International Conference on Fibonacci Numbers and Their Applications’, Pisa, Italy, July 25–29, 1988

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Front Matter....Pages i-xxiv
The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations....Pages 1-6
A GCD Property on Pascal’s Pyramid and the Corresponding LCM Property of the Modified Pascal Pyramid....Pages 7-14
Translatable and Rotatable Configurations which Give Equal Product, Equal GCD and Equal LCM Properties Simultaneously....Pages 15-26
Fibonacci Length of Generating Pairs in Groups....Pages 27-35
A Generalization of Fibonacci Trees....Pages 37-56
Generalized Fibonacci Numbers are Rounded Powers....Pages 57-62
On Generalized Fibonacci Numbers of Graphs....Pages 63-76
An Investigation of Sequences Derived from Hoggatt Sums and Hoggatt Triangles....Pages 77-88
Representation of Natural Numbers as Sums of Fibonacci Numbers: An Application to Modern Cryptography....Pages 89-99
A Note on Ramifications Concerning the Construction of Pythagorean Triples from Recursive Sequences....Pages 101-106
On the Representation of {F kn /F n }, {F kn /L n }, {L kn /L n }, and {L kn /F n } as Zeckendorf Sums....Pages 107-114
Functional Recurrences....Pages 115-121
Concentric Cycles in Mosaic Graphs....Pages 123-128
Fibonacci Triangles....Pages 129-132
Mosaic Numbers of Fibonacci Trees....Pages 133-138
Falling Factorial Polynomials of Generalized Fibonacci Type....Pages 139-153
Some Notes on Fibonacci Binary Sequences....Pages 155-160
Congruences for Weighted and Degenerate Stirling Numbers....Pages 161-170
An Inverse Theorem on Fibonacci Numbers....Pages 171-179
Some Results on Divisibility Sequences....Pages 181-189
On Mental Calculation of Repeating Decimals, Finding Fibonacci Numbers and a Connection to Pascal’s Triangle....Pages 191-195
Diophantine Representation of Fibonacci Numbers Over Natural Numbers....Pages 197-201
On Prime Divisors of the Terms of Second Order Linear Recurrence Sequences....Pages 203-207
An Alternating Product Representation for Real Numbers....Pages 209-216
Maximum Length of the Euclidean Algorithm and Continued Fractions in F (X)....Pages 217-222
Recurrence Relations in Sinusoids and Their Applications to Spectral Analysis and to the Resolution of Algebraic Equations....Pages 223-238
A Recurrence Relation for Gaussian Multinomial Coefficients....Pages 239-240
Some Binomial Fibonacci Identities....Pages 241-254
A Survey of Properties of Third Order Pell Diagonal Functions....Pages 255-271
Multivariate Fibonacci Polynomials of Order K and the Multiparameter Negative Binomial Distribution of the Same Order....Pages 273-279
Longest Circular Runs with an Application in Reliability Via the Fibonacci-Type Polynomials of Order K....Pages 281-286
Fibonacci Numbers and an Algorithm of Lemoine and Kátai....Pages 287-297
Generalizations of Sequences of Lucas and Bell....Pages 299-309
Distribution of Residues of Certain Second-Order Linear Recurrences Modulo P....Pages 311-324
The Fibonacci Tree, Hofstadter and the Golden String....Pages 325-334
Three Number Trees - Their Growth Rules and Related Number Properties....Pages 335-350
Back Matter....Pages 351-357