Aritmetické vlastnosti Fibonacciových čísel
Asymptotic form for generalized factorial
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.
Bartz-Marlewski equation with generalized Lucas components
Let and be the Lucas sequences of the first and second kind respectively at the parameters and . In this paper, we provide a technique for characterizing the solutions of the so-called Bartz-Marlewski equation where or with , . Then, the procedure of this technique is applied to completely resolve this equation with certain values of such parameters.
Bell polynomials and degenerate stirling numbers
Bender's generalized q-binominal Vandermonde convolution.
Berechnung der Werte von Zetafunktionen totalreeller kubischer Zahlkörper an ganzzahligen Stellen mittels verallgemeinerter Dedekindscher Summen. I.
Bihyperbolic numbers of the Fibonacci type and their idempotent representation
In this paper we introduce bihyperbolic numbers of the Fibonacci type. We present some of their properties using matrix generators and idempotent representations.
Binomials transformation formulae for scaled Fibonacci numbers
The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
Bounds for frequencies of residues of second-order recurrences modulo
The authors examine the frequency distribution of second-order recurrence sequences that are not -regular, for an odd prime , and apply their results to compute bounds for the frequencies of -singular elements of -regular second-order recurrences modulo powers of the prime . The authors’ results have application to the -stability of second-order recurrence sequences.
Can a Lucas number be a sum of three repdigits?
We give the answer to the question in the title by proving that is the largest Lucas number expressible as a sum of exactly three repdigits. Therefore, there are many Lucas numbers which are sums of three repdigits.
Cartan Bernoulli Numbers as Values of L-Series.
Catalan numbers, the Hankel transform, and Fibonacci numbers.
Catalan's identity and Chebyshev polynomials of the second kind.
Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences
In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.
Certain matrices related to Fibonacci sequence having recursive entries.
Cinq nombres dont les sommes deux à deux sont des carrés
Cipolla pseudoprimes.
Circulants and the factorization of the Fibonacci–like numbers
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues.
Classifying Lehmer triples