Results 11 to 20 of about 3,220 (237)
On perfect powers in $k$-generalized Pell sequence [PDF]
Mathematica Bohemica, 2023 Let $k\geq2$ and let $(P_n^{(k)})_{n\geq2-k}$ be the $k$-generalized Pell sequence defined by \begin{equation*} P_n^{(k)}=2P_{n-1}^{(k)}+P_{n-2}^{(k)}+\cdots+P_{n-k}^{(k)} \end{equation*}for $n\geq2$ with initial conditions \begin{equation*} P_{-(k-2)}^{(
Zafer Şiar +2 more
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Mulatu Numbers Which Are Concatenation of Two Fibonacci Numbers
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023 Let (M_k) be the sequence of Mulatu numbers defined by M_0=4, M_1=1, M_k=M_(k-1)+M_(k-2) and (F_k) be the Fibonacci sequence given by the recurrence F_k=F_(k-1)+F_(k-2) with the initial conditions F_0=0, F_1=1 for k≥2.
Fatih Erduvan, Merve Güney Duman
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Fractional parts of powers of real algebraic numbers
Comptes Rendus. Mathématique, 2022 Let $\alpha $ be a real algebraic number greater than $1$. We establish an effective lower bound for the distance between an integral power of $\alpha $ and its nearest integer.
Bugeaud, Yann
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Repdigits as difference of two Fibonacci or Lucas numbers
Математичні Студії, 2021 In the present study we investigate all repdigits which are expressed as a difference of two Fibonacci or Lucas numbers. We show that if $F_{n}-F_{m}$ is a repdigit, where $F_{n}$ denotes the $n$-th Fibonacci number, then $(n,m)\in \{(7,3),(9,1),(9,2 ...
P. Ray, K. Bhoi
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Fermat $k$-Fibonacci and $k$-Lucas numbers [PDF]
Mathematica Bohemica, 2020 Using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and Pethő, we find all $k$-Fibonacci and $k$-Lucas numbers which are Fermat numbers.
Jhon J. Bravo, Jose L. Herrera
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Repdigits as Product of Terms of k-Bonacci Sequences
Mathematics, 2021 For any integer k≥2, the sequence of the k-generalized Fibonacci numbers (or k-bonacci numbers) is defined by the k initial values F−(k−2)(k)=⋯=F0(k)=0 and F1(k)=1 and such that each term afterwards is the sum of the k preceding ones.
Petr Coufal, Pavel Trojovský
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On Homogeneous Combinations of Linear Recurrence Sequences
Mathematics, 2020 Let (Fn)n≥0 be the Fibonacci sequence given by Fn+2=Fn+1+Fn, for n≥0, where F0=0 and F1=1. There are several interesting identities involving this sequence such as Fn2+Fn+12=F2n+1, for all n≥0. In 2012, Chaves, Marques and Togbé proved that if (Gm)m is a
Marie Hubálovská +2 more
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Fibonacci Numbers with a Prescribed Block of Digits
Mathematics, 2020 In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from ...
Pavel Trojovský
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Almost Repdigit k-Fibonacci Numbers with an Application of k-Generalized Fibonacci Sequences
Mathematics, 2023 In this paper, we define the notion of almost repdigit as a positive integer whose digits are all equal except for at most one digit, and we search all terms of the k-generalized Fibonacci sequence which are almost repdigits. In particular, we find all k-
Alaa Altassan, Murat Alan
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Repdigits as Product of Fibonacci and Tribonacci Numbers
Mathematics, 2020 In this paper, we study the problem of the explicit intersection of two sequences. More specifically, we find all repdigits (i.e., numbers with only one repeated digit in its decimal expansion) which can be written as the product of a Fibonacci by a ...
Dušan Bednařík, Eva Trojovská
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