Results 51 to 60 of about 10,886,718 (351)
On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
, 2010 We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers.
Bilu +13 more
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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
doaj +1 more source
q-Congruences, with applications to supercongruences and the cyclic sieving phenomenon
, 2019 We establish a supercongruence conjectured by Almkvist and Zudilin, by proving a corresponding $q$-supercongruence. Similar $q$-supercongruences are established for binomial coefficients and the Ap\'{e}ry numbers, by means of a general criterion ...
Gorodetsky, Ofir
core +1 more source
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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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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Fibonacci–Lucas–Pell–Jacobsthal relations
Annales Mathematicae et Informaticae, 2022 In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant ...
R. Frontczak, T. Goy, M. Shattuck
semanticscholar +1 more source
On some series involving the binomial coefficients $binom{3n}{n}$ [PDF]
Notes on Number Theory and Discrete MathematicsUsing a simple transformation, we obtain much simpler forms for some series involving binomial coefficients $binom{3n}{n}$ derived by Necdet Batir. New evaluations are given and connections with Fibonacci numbers and the golden ratio are established ...
Kunle Adegoke +2 more
doaj +1 more source
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
doaj +1 more source
Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]
, 2014 In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a prime, $n=n_0 ...
Meštrović, Romeo
core
Pediatric Blood &Cancer, EarlyView.ABSTRACT Anaplastic sarcoma of the kidney (ASK) is a DICER1‐associated malignant tumor presumed to arise in a benign precursor, pediatric cystic nephroma (PCN). However, the initial oncogenic alteration(s) associated with malignant transformation are unknown.
Nahir Cortes‐Santiago +6 more
wiley +1 more source