Results 21 to 30 of about 594,288 (306)
Three new classes of binomial Fibonacci sums [PDF]
Transactions on CombinatoricsIn 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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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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Special Matrices, 2020 In this paper, our main attention is paid to calculate the determinants and inverses of two types Toeplitz and Hankel tridiagonal matrices with perturbed columns.
Fu Yaru +3 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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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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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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On Hybrid Hyper k-Pell, k-Pell–Lucas, and Modified k-Pell Numbers
Axioms, 2023 Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems.
Elen Viviani Pereira Spreafico +2 more
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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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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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Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture
Open Mathematics, 2023 We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer k≥2k\ge 2, there are ≫logx\gg \hspace{0.25em}\log x Lucas non-Wieferich primes p≤xp\le x such that p≡±1(modk)p\equiv ...
Anitha K. +2 more
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