Results 1 to 10 of about 975,688 (231)
Lucas factoriangular numbers [PDF]
Mathematica Bohemica, 2020 We show that the only Lucas numbers which are factoriangular are $1$ and $2$.
Bir Kafle, Florian Luca, Alain Togbé
doaj +4 more sources
Journal of Mathematical Sciences and Modelling, 2021 Since people existed, they have prioritized confidentiality in information sharing and communication. Although there are independent studies on encryption and music in literature, no study is seen on encryption methods that are created by using the ...
Firdevs Nur Algül +2 more
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Multiple extensions of a finite Euler's pentagonal number theorem and the Lucas formulas [PDF]
, 2007 Motivated by the resemblance of a multivariate series identity and a finite analogue of Euler's pentagonal number theorem, we study multiple extensions of the latter formula.
Andrews +16 more
core +3 more sources
Fibonacci or Lucas numbers that are products of two Lucas numbers or two Fibonacci numbers [PDF]
arXiv, 2023 This contribution presents all possible solutions to the Diophantine equations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers that are the product of two arbitrary Lucas numbers and Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein. The results under consideration are proven by using Dujella-Peth\
Daşdemir, Ahmet, Emin, Ahmet
arxiv +3 more sources
The extended Frobenius problem for Lucas series incremented by a Lucas number
, 2022 We study the extended Frobenius problem for sequences of the form $\{l_a\}\cup\{l_a+l_n\}_{n\in\mathbb{N}}$ and $\{l_a+l_n\}_{n\in\mathbb{N}}$, where $\{l_n\}_{n\in\mathbb{N}}$ is the Lucas series and $l_a$ is a Lucas number.
Robles-Pérez, Aureliano M. +1 more
core +3 more sources
The Lucas property of a number array
Discrete Mathematics, 2002 AbstractFor all nonnegative integers i,j let w(i,j|a,b,c) denote the number of all paths in the plane from (0,0) to (i,j) with steps (1,0), (0,1), (1,1), and with positive integer weights a, b, c, respectively. The divisibility property of the array w(i,j|a,b,c) is studied.
Marko Razpet
openalex +3 more sources
ALTERED NUMBERS OF LUCAS NUMBER SQUARED
Journal of Scientific Reports-A, 2023 We investigate two types altered Lucas numbers denoted and defined by adding or subtracting a value from the square of the Lucas numbers. We achieve these numbers form as the consecutive products of the Fibonacci numbers. Therefore, consecutive sum-subtraction relations of altered Lucas numbers and their Binet-like formulas are given by using ...
Fikri Köken, Emre KANKAL
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Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients
Universal Journal of Mathematics and Applications, 2023 In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, and exponential generating functions for these numbers. Then we define an associate matrix for these numbers.
Emrah Polatlı
doaj +3 more sources
Lucas' theorem: its generalizations, extensions and applications (1878--2014) [PDF]
arXiv, 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 +1 more source
Incomplete Tribonacci-Lucas numbers and polynomials [PDF]
Advances in Applied Clifford Algebras, 25(3), 2015, 2014 In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function
Necati Taskara, Nazmiye Yilmaz
arxiv +5 more sources