Results 41 to 50 of about 975,787 (327)
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
Agronomy Journal, Volume 114, Issue 6, Page 3544-3553, November/December 2022., 2022 Abstract Bermudagrass [Cynodon dactylon (L.) Pers.] is one of the most widely cultivated turfgrass species throughout the world. It has several important attributes, such as heat and drought tolerance, and one big disadvantage, which is susceptibility to cold temperatures.
Diego Gómez de Barreda +3 more
wiley +1 more source
On harmonic numbers and Lucas sequences [PDF]
Publicationes Mathematicae Debrecen, 2012 Harmonic numbers $H_k=\sum_{05 we have $$\sum_{k=0}^{p-1}u_{k+ }H_k/2^k=0 (mod p),$$ where $ =0$ if p=1,2,4,8 (mod 15), and $ =1$ otherwise.
openaire +3 more sources
Generalized Bernoulli Numbers and a Formula of Lucas [PDF]
The Fibonacci Quarterly, 2015 An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The value of this sum is then given in terms of the Meixner-Pollaczek polynomials.
Moll, Victor H., Vignat, Christophe
openaire +3 more sources
AIChE Journal, Volume 69, Issue 1, January 2023., 2023 Abstract Lignin‐rich stream from lignocellulosic ethanol production was converted into biocrude by continuous hydrothermal liquefaction (HTL) while hydrogen was produced by aqueous phase reforming (APR) of the HTL aqueous by‐product. The effects of Na2CO3 and NaOH were investigated both in terms of processability of the feedstock as well as yield and ...
Arturo Di Fraia +8 more
wiley +1 more source
Gaussian Mersenne Lucas numbers and polynomials [PDF]
arXiv, 2023 In the present article we introduce three new notions which are called Gaussian Mersenne Lucas numbers, Mersenne Lucas polynomials and Gaussian Mersenne Lucas polynomials. We present and prove our exciting properties and results of them such as: recurrence relations, Binet's formulas, explicit formulas, generating functions, symmetric functions and ...
arxiv
On square Tribonacci Lucas numbers
Hacettepe Journal of Mathematics and Statistics, 2021 The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
openaire +2 more sources
On some new results for the generalised Lucas sequences
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021 In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits ...
Andrica Dorin +2 more
doaj +1 more source
, 2000 In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of
Saidak, F.
core +1 more source
Environmental Research Letters, 2023 We present a new application to recognize 218 species of cultivated crops on geo-tagged photos, ‘Pl@ntNet Crops’. The application and underlying algorithms are developed using more than 750k photos voluntarily collected by Pl@ntNet users. The app is then
M van der Velde +13 more
doaj +1 more source