Results 11 to 20 of about 594,288 (306)
On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
Integers, 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
core +6 more sources
The Lucas property of a number array
Discrete Mathematics, 2002 Let \(p\) be a prime and \(\alpha\), \(\beta\), \(\gamma\), \(\delta\) be nonnegative integers such that \(0\leq \beta< p\) and \(0\leq\delta< p\). A double integer number array \(N(i,j)\), where \(i\) and \(j\) are nonnegative integers, is said to satisfy the Lucas property, if \(N(\alpha p+\beta, \gamma p+\delta)\equiv N(\alpha, \gamma)N(\beta,\delta)
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
openalex +5 more sources
On Bicomplex Pell and Pell-Lucas Numbers
Communications in Advanced Mathematical Sciences, 2018 In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected between ...
Fügen Torunbalcı Aydın
doaj +4 more sources
The extended Frobenius problem for Lucas series incremented by a Lucas number [PDF]
Quaestiones Mathematicae13 pages.
Aureliano M. Robles-Pérez +1 more
openalex +4 more sources
On divisors of Lucas and Lehmer numbers [PDF]
Acta Mathematica, 2013 Let u(n) be the n-th term of a Lucas sequence or a Lehmer sequence.In this article we shall establish an estimate from below for the greatest prime factor of u(n) which is of the form nexp(logn/104loglogn). In so doing we are able to resolve a question of Schinzel from 1962 and a conjecture of Erdos from 1965.In addition we are able to give the first ...
openaire +3 more sources
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
openaire +2 more sources
On the reciprocal sum of the fourth power of Fibonacci numbers
Open Mathematics, 2022 Let fn{f}_{n} be the nnth Fibonacci number with f1=f2=1{f}_{1}={f}_{2}=1. Recently, the exact values of ∑k=n∞1fks−1⌊{\left({\sum }_{k=n}^{\infty }\frac{1}{{f}_{k}^{s}}\right)}^{-1}⌋ have been obtained only for s=1,2s=1,2, where ⌊x⌋\lfloor x\
Hwang WonTae +2 more
doaj +1 more source
Some new identities of a type of generalized numbers involving four parameters
AIMS Mathematics, 2022 This article deals with a Horadam type of generalized numbers involving four parameters. These numbers generalize several celebrated numbers in the literature such as the generalized Fibonacci, generalized Lucas, Fibonacci, Lucas, Pell, Pell-Lucas ...
Waleed Mohamed Abd-Elhameed +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