Results 31 to 40 of about 10,192,155 (339)

Fibonacci and Lucas Polynomials in n-gon

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2023
In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices.
B. Kuloǧlu, E. Özkan, M. Marin
semanticscholar   +1 more source

p-Analogue of biperiodic Pell and Pell–Lucas polynomials

Notes on Number Theory and Discrete Mathematics, 2023
In this study, a binomial sum, unlike but analogous to the usual binomial sums, is expressed with a different definition and termed the p-integer sum. Based on this definition, p-analogue Pell and Pell–Lucas polynomials are established and the generating
B. Kuloǧlu, E. Özkan, A. Shannon
semanticscholar   +1 more source

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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Formulae of the Frobenius number in relatively prime three Lucas numbers [PDF]

Songklanakarin Journal of Science and Technology (SJST), 2020
In this paper, we find the explicit formulae of the Frobenius number for numerical semigroups generated by relatively prime three Lucas numbers 2 , L L i i and Lil  for given integers i ≥ 3, l ≥ 4 .
Ratchanok Bokaew, Boonrod Yuttanan, Sukrawan Mavecha   +2 more
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On Bicomplex Jacobsthal-Lucas Numbers

Journal of Mathematical Sciences and Modelling, 2020
In this study we introduced a sequence of bicomplex numbers whose coefficients are chosen from the sequence of Jacobsthal-Lucas numbers. We also present some identities about the known some fundamental identities such as the Cassini's, Catalan's and Vajda's identities.
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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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On the reciprocal sum of the fourth power of Fibonacci numbers

Open Mathematics, 2022
Let fn{f}_{n} be the nnth Fibonacci number with f1=f2=1{f}_{1}={f}_{2}=1. Recently, the exact values of ∑k=n∞1fks−1⌊{\left({\sum }_{k=n}^{\infty }\frac{1}{{f}_{k}^{s}}\right)}^{-1}⌋ have been obtained only for s=1,2s=1,2, where ⌊x⌋\lfloor x\
Hwang WonTae, Park Jong-Do, Song Kyunghwan   +2 more
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ON DUAL BICOMPLEX BALANCING AND LUCAS-BALANCING NUMBERS

Journal of Science and Arts, 2023
In this paper, dual bicomplex Balancing and Lucas-Balancing numbers are defined, and some identities analogous to the classic properties of the Fibonacci and Lucas sequences are produced.
M. Uysal, Engin Özkan, Anthony G. Shannon   +2 more
semanticscholar   +1 more source

Practical numbers in Lucas sequences [PDF]

Quaestiones Mathematicae, 2018
A practical number is a positive integer n such that all the positive integers m ≤ n can be written as a sum of distinct divisors of n. Let (un)n≥0 be the Lucas sequence satisfying u0 = 0, u1 = 1, and un+2 = aun+1 + bun for all integers n ≥ 0, where a and b are fixed nonzero integers. Assume a(b + 1) even and a 2 + 4b > 0.
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Counting divisors of Lucas numbers [PDF]

Pacific Journal of Mathematics, 1998
Let \(L_n\) be the sequence of Lucas numbers defined by \(L_0= 2\), \(L_1= 1\) and \(L_n= L_{n-1}+ L_{n-2}\). We say a positive integer \(m\) is a divisor of this sequence if \(m\) divides a Lucas number. The author investigates the density of the set of divisors of the Lucas sequence. The main result of the paper is: Theorem 1. Let \({\mathcal L}(x)\)
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