Results 11 to 20 of about 1,121 (104)
An exponential Diophantine equation related to the difference between powers of two consecutive Balancing numbers [PDF]
, 2018 In this paper, we find all solutions of the exponential Diophantine equation $B_{n+1}^x-B_n^x=B_m$ in positive integer variables $(m, n, x)$, where $B_k$ is the $k$-th term of the Balancing sequence.Comment: Comments are ...
Faye, Bernadette +3 more
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Discussiones Mathematicae - General Algebra and Applications, 2018 In this paper we introduce the Horadam hybrid numbers and give some their properties: Binet formula, character and generating function.
Szynal-Liana Anetta
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A Family of the Zeckendorf Theorem Related Identities [PDF]
, 2015 In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation.
Martinjak, Ivica
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Extended Fibonacci numbers and polynomials with probability applications
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 50, Page 2681-2693, 2004., 2004 The extended Fibonacci sequence of numbers and polynomials is introduced and studied. The generating function, recurrence relations, an expansion in terms of multinomial coefficients, and several properties of the extended Fibonacci numbers and polynomials are obtained.
Demetrios L. Antzoulakos
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2507-2518, 2003., 2003 We prove that powers of 4‐netted matrices (the entries satisfy a four‐term recurrence δai,j = αai−1,j + βai−1,j + γai,j−1) preserve the property of nettedness: the entries of the eth power satisfy δeai,j(e)=αeai−1,j(e)+βeai−11,j−(e)+γeai,j−1(e), where the coefficients are all instances of the same sequence xe+1 = (β + δ)xe − (βδ + αγ)xe−1.
Pantelimon Stănică
wiley +1 more source
A Study on Fibonacci and Lucas Bihypernomials
Discussiones Mathematicae - General Algebra and Applications, 2022 The bihyperbolic numbers are extension of hyperbolic numbers to four dimensions. In this paper we introduce and study the Fibonacci and Lucas bihypernomials, i.e., polynomials, which are a generalization of the bihyperbolic Fibonacci numbers and the ...
Szynal-Liana Anetta, Włoch Iwona
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On the greatest common divisor of $n$ and the $n$th Fibonacci number [PDF]
, 2017 Let $\mathcal{A}$ be the set of all integers of the form $\gcd(n, F_n)$, where $n$ is a positive integer and $F_n$ denotes the $n$th Fibonacci number.
Leonetti, Paolo, Sanna, Carlo
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A note on Fibonacci matrices of even degree
International Journal of Mathematics and Mathematical Sciences, Volume 27, Issue 8, Page 457-469, 2001., 2001 This paper presents a construction of m‐by‐m irreducible Fibonacci matrices for any even m. The proposed technique relies on matrix representations of algebraic number fields which are an extension of the golden section field. The explicit construction of some 6‐by‐6 and 8‐by‐8 irreducible Fibonacci matrices is given.
Michele Elia
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On the power sum problem of Lucas polynomials and its divisible property
Open Mathematics, 2018 The main purpose of this paper is to use the mathematical induction and the properties of Lucas polynomials to study the power sum problem of Lucas polynomials. In the end, we obtain an interesting divisible property.
Xiao Wang
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Annales Mathematicae Silesianae, 2020 Let {rn}n∈ be a strictly increasing sequence of nonnegative real numbers satisfying the asymptotic formula rn ~ αβn, where α, β are real numbers with α > 0 and β > 1. In this note we prove some limits that connect this sequence to the number e.
Farhadian Reza, Jakimczuk Rafael
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