Results 111 to 120 of about 1,083 (122)

Some alternating sums of Lucas numbers

Open Mathematics, 2005
Čerin Zvonko
doaj   +1 more source

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Markov triples with two Fibonacci components

Rendiconti del Seminario Matematico della Universita di Padova, 2022
In this paper, we prove that there are at most finitely many pairs of Fibonacci numbers (x, y) = (Fm, Fn) with the property that m ≤ n and the pair (m,n) 6∈ {(1, 2r− 1), (1, 2), (2, 2r+ 1), (2r+ 1, 2r+ 3) : r ≥ 1} such that (x, y, z) is a Markov triple ...
F. Luca
semanticscholar   +1 more source

A generalized quaternion with generalized Fibonacci number components

, 2020
In this paper we introduce a generalized quaternion with generalized Fibonacci number components. For this quaternion we obtain the two types of Catalan’s identities and d’Ocagne’s identity.
Y. Choo
semanticscholar   +1 more source

Generalized Tribonacci Sequence and its Sum Through Third Order Difference Operator

2024 International Conference on Science, Engineering and Business for Driving Sustainable Development Goals (SEB4SDG)
This study presents the generalized third-order difference operator with constant coefficients and inverse, allowing us to construct a sequence similar to the generalized k-Fibonacci sequence.
Rajiniganth P, A. T, Oluwayemi M. O, Oyetepo T, Suresh K   +4 more
semanticscholar   +1 more source

On Triangles With Fibonacci and Lucas Numbers as Coordinates

Sarajevo Journal of Mathematics
We consider triangles in the plane with coordinates of points from the Fibonacci and Lucas sequences.
Z. Čerin
semanticscholar   +1 more source

Pencils of Euler Triples, I

Sarajevo Journal of Mathematics
In this paper we will study the families of triples $(u,v,w)$ of elements in a commutative ring $r$ with the property that $v\,w+n=\widetilde{u}^2$, $w\,u+n=\widetilde{v}^2$ and $u\,v+n=\widetilde{w}^2$ for some $n, ...
Z. Čerin
semanticscholar   +1 more source

Powers of balancing polynomials and some consequences for Fibonacci sums

International Journal of Mathematical Analysis, 2019
In this short article, we derive identities for powers of balancing and Lucas-balancing polynomials. These polynomials are a natural extension of balancing and Lucas-balancing numbers.
R. Frontczak
semanticscholar   +1 more source

On the reciprocal sums of generalized Fibonacci numbers

, 2016
In this paper we obtain some identities for the infinite sum of the reciprocal generalized Fibonacci numbers and the infinite sum of the square of the reciprocal generalized Fibonacci numbers.
Y. Choo
semanticscholar   +1 more source

Some results on a generalized bi-periodic Lucas sequence

, 2020
In this paper we consider a generalized bi-periodic Lucas sequence introduced by Bilgici. For this sequence we derive the Catalan’s identity and Gelin-Cesàro identity.
Y. Choo
semanticscholar   +1 more source

New generalizations of Fibonacci and Lucas sequences

, 2014
We consider the sequences { } and { } which are generated by the recurrence relations ( ) and ( ) with the initial conditions and where a and b are any non – zero real numbers.
Göksal Bilgici
semanticscholar   +1 more source