Results 41 to 50 of about 10,192,155 (339)
A class of numbers associated with the Lucas numbers
Mathematical and Computer Modelling, 1997 Motivated essentially by a recent work of \textit{A. K. Agarwal} [Fibonacci Q. 28, 194-199 (1990; Zbl 0713.11015)], the main object of this paper is to present a systematic investigation of a new class of numbers associated with the familiar Lucas numbers.
R. K. Raina, Hari M. Srivastava
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Weighted sum of the sixth powers of Horadam numbers [PDF]
Notes on Number Theory and Discrete MathematicsOhtsuka and Nakamura found simple formulas for Σⁿⱼ₌₁Fⱼ⁶ and Σⁿⱼ₌₁Lⱼ⁶, where Fₖ and Lₖ are the k-th Fibonacci and Lucas numbers, respectively. In this note we extend their results to a general second order sequence by deriving a formula for Σⁿⱼ₌₁(-1/q³ ...
Kunle Adegoke +2 more
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Some new identities of a type of generalized numbers involving four parameters
AIMS Mathematics, 2022 This article deals with a Horadam type of generalized numbers involving four parameters. These numbers generalize several celebrated numbers in the literature such as the generalized Fibonacci, generalized Lucas, Fibonacci, Lucas, Pell, Pell-Lucas ...
Waleed Mohamed Abd-Elhameed +2 more
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On the k-Mersenne–Lucas numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2021 In this paper, we will introduce a new definition of k-Mersenne–Lucas numbers and investigate some properties. Then, we obtain some identities and established connection formulas between k-Mersenne–Lucas numbers and k-Mersenne numbers through the use of Binet’s formula.
Ali Boussayoud, Mourad Chelgham
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A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Demonstratio Mathematica, 2016 We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2.
Laugier Alexandre, Saikia Manjil P.
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Some Applications of Fibonacci and Lucas Numbers [PDF]
, 2021 In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary relation over the real fields instead of addition of the real numbers and we give properties of the new obtained ...
Cristina Flaut +2 more
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The Frobenius Number for Jacobsthal Triples Associated with Number of Solutions
Axioms, 2023 In this paper, we find a formula for the largest integer (p-Frobenius number) such that a linear equation of non-negative integer coefficients composed of a Jacobsthal triplet has at most p representations.
T. Komatsu, C. Pita-Ruiz
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On harmonic numbers and Lucas sequences [PDF]
Publicationes Mathematicae Debrecen, 2012 Harmonic numbers $H_k=\sum_{05 we have $$\sum_{k=0}^{p-1}u_{k+ }H_k/2^k=0 (mod p),$$ where $ =0$ if p=1,2,4,8 (mod 15), and $ =1$ otherwise.
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On the l.c.m. of shifted Lucas numbers
Indagationes Mathematicae, 2022 Let $(L_n)_{n \geq 1}$ be the sequence of Lucas numbers, defined recursively by $L_1 := 1$, $L_2 := 3$, and $L_{n + 2} := L_{n + 1} + L_n$, for every integer $n \geq 1$. We determine the asymptotic behavior of $\log \operatorname{lcm} (L_1 + s_1, L_2 + s_2, \dots, L_n + s_n)$ as $n \to +\infty$, for $(s_n)_{n \geq 1}$ a periodic sequence in $\{-1, +1\}$
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Fibonacci or Lucas numbers that are products of two Lucas numbers or two Fibonacci numbers
, 2023 This contribution presents all possible solutions to the Diophantine equations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers that are the product of two arbitrary Lucas numbers and Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein.
Daşdemir, Ahmet, Emin, Ahmet
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