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Primitive divisors of Lucas and Lehmer sequences [PDF]
, 1995 Stewart reduced the problem of determining all Lucas and Lehmer sequences whose $n$-th element does not have a primitive divisor to solving certain Thue equations.
Par Paul M Voutier, Paul M. Voutier
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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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Mathematics, 2019 Foeplitz and Loeplitz matrices are Toeplitz matrices with entries being Fibonacci and Lucas numbers, respectively. In this paper, explicit expressions of determinants and inverse matrices of Foeplitz and Loeplitz matrices are studied.
Zhaolin Jiang +4 more
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The density of numbers $n$ having a prescribed G.C.D. with the $n$th Fibonacci number [PDF]
, 2018 For each positive integer $k$, let $\mathscr{A}_k$ be the set of all positive integers $n$ such that $\gcd(n, F_n) = k$, where $F_n$ denotes the $n$th Fibonacci number.
Sanna, Carlo, Tron, Emanuele
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Demography of sea lamprey (Petromyzon marinus) ammocoete populations in relation to potential spawning-migration obstructions [PDF]
, 2017 Copyright © 2017 John Wiley & Sons, Ltd. Recent advances in the understanding of lamprey migrations have led to concerns over the impacts of obstructions on the demography of many species. This study investigated sea lamprey (Petromyzon marinus) larvae
Bolland, J. D. +5 more
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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
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Development of visible light‐sensitive human neuropsin (OPN5) via single amino acid substitution
FEBS Letters, EarlyView.The present study determines a key amino acid residue, Lys91, for defining UV sensitivity of human OPN5. Heterologous action spectroscopy of the wild type and K91 mutants of OPN5 in HEK293T cells reveals that substitution of Lys91 with neutral (alanine) or acidic amino acids (glutamic or aspartic acids) causes substantial shifts in spectral sensitivity
Yusuke Sakai +2 more
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Indagationes Mathematicae, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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An identity for the Fibonacci and Lucas numbers [PDF]
Glasgow Mathematical Journal, 1993 In this paper we prove an identity between sums of reciprocals of Fibonacci and Lucas numbers. The Fibonacci numbers are defined for all n ≥ 0 by the recurrence relation Fn + 1 = Fn + Fn-1 for n ≥ 1, where F0 = 0 and F1 = 0. The Lucas numbers Ln are defined for all n ≥ 0 by the same recurrence relation, where L0 = 2 and L1 = 1 We prove the following ...
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