Results 11 to 20 of about 625,251 (324)

Construction of dual-generalized complex Fibonacci and Lucas quaternions

Karpatsʹkì Matematičnì Publìkacìï, 2022
The aim of this paper is to construct dual-generalized complex Fibonacci and Lucas quaternions. It examines the properties both as dual-generalized complex number and as quaternion. Additionally, general recurrence relations, Binet's formulas, Tagiuri's (
G.Y. Şentürk, N. Gürses, S. Yüce
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Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers [PDF]

Czechoslovak Mathematical Journal, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carlip, W., Somer, L.
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Exact divisibility by powers of the integers in the Lucas sequence of the first kind

AIMS Mathematics, 2020
Lucas sequence of the first kind is an integer sequence $(U_n)_{n\geq0}$ which depends on parameters $a,b\in\mathbb{Z}$ and is defined by the recurrence relation $U_0=0$, $U_1=1$, and $U_n=aU_{n-1}+bU_{n-2}$ for $n\geq2$. In this article, we obtain exact
Kritkhajohn Onphaeng, Prapanpong Pongsriiam   +1 more
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Some new properties of hyperbolic k-Fibonacci and k-Lucas octonions [PDF]

Notes on Number Theory and Discrete Mathematics
The aim of this paper is to establish some novel identities for hyperbolic k-Fibonacci octonions and k-Lucas octonions. We prove these properties using the identities of k-Fibonacci and k-Lucas numbers, which we determined previously.
A. D. Godase
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Incomplete Tribonacci–Lucas Numbers and Polynomials [PDF]

Advances in Applied Clifford Algebras, 2014
In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function
Yilmaz, Nazmiye, Taskara, Necati
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Erdos Conjecture I. [PDF]

, 2000
In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of
Saidak, F.
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On square Tribonacci Lucas numbers

Hacettepe Journal of Mathematics and Statistics, 2021
The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
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Three new classes of binomial Fibonacci sums [PDF]

Transactions on Combinatorics
In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal The Fibonacci Quarterly.
Robert Frontczak
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Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu, Naime Şeyda Türkoğlu   +1 more
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Lucas numbers of the form PX2, where P is prime

International Journal of Mathematics and Mathematical Sciences, 1991
Let Ln denote the nth Lucas number, where n is a natural number.
Neville Robbins
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