Results 21 to 30 of about 626,146 (282)
Sums of Pell/Lucas Polynomials and Fibonacci/Lucas Numbers
Mathematics, 2022 Seven infinite series involving two free variables and central binomial coefficients (in denominators) are explicitly evaluated in closed form. Several identities regarding Pell/Lucas polynomials and Fibonacci/Lucas numbers are presented as consequences.
Dongwei Guo, Wenchang Chu
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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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Series associated with harmonic numbers, Fibonacci numbers and central binomial coefficients $binom{2n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsWe find various series that involve the central binomial coefficients $binom{2n}{n}$, harmonic numbers and Fibonacci numbers. Contrary to the traditional hypergeometric function _pF_q approach, our method utilizes a straightforward transformation to ...
Segun Olofin Akerele +1 more
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Balancing and Lucas-Balancing Numbers and their Application to Cryptography [PDF]
, 2016 It is well known that, a recursive relation for the sequence  is an equation that relates  to certain of its preceding terms .
Kumar Ray, Prasanta +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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Incomplete Bivariate Fibonacci and Lucas 𝑝-Polynomials
Discrete Dynamics in Nature and Society, 2012 We define the incomplete bivariate Fibonacci and Lucas 𝑝-polynomials. In the case 𝑥=1, 𝑦=1, we obtain the incomplete Fibonacci and Lucas 𝑝-numbers. If 𝑥=2, 𝑦=1, we have the incomplete Pell and Pell-Lucas 𝑝-numbers.
Dursun Tasci +2 more
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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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, 2021 {"references": ["1.\tR. Sivaraman, Number Triangles and Metallic Ratios, International Journal of Engineering and Computer Science, Volume 10, Issue 8, pp. 25365 \u2013 25369. 2.\tR. Sivaraman, Generalized Pascal's Triangle and Metallic Ratios, International Journal of Research, Volume 9, Issue 7, pp. 179 \u2013 184. 3.\tR.
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Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 2022 The present work aims to introduce and study the Gaussian Bronze Lucas number sequence. Firstly, we define Gaussian Bronze Lucas numbers by extending the Bronze Lucas numbers. Then, we find the Binet formula and generating function for this number sequence. We also investigate some sum formulas and matrices related to the Gaussian Bronze Lucas numbers.
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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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