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Markov triples with two Fibonacci components
Rendiconti del Seminario Matematico della Universita di Padova, 2022In 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
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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
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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
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On Triangles With Fibonacci and Lucas Numbers as Coordinates
Sarajevo Journal of MathematicsWe consider triangles in the plane with coordinates of points from the Fibonacci and Lucas sequences.
Z. Čerin
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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 +4 more
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A generalized quaternion with generalized Fibonacci number components
, 2020In 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
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Powers of balancing polynomials and some consequences for Fibonacci sums
International Journal of Mathematical Analysis, 2019In 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
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On the reciprocal sums of generalized Fibonacci numbers
, 2016Y. Choo
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New generalizations of Fibonacci and Lucas sequences
, 2014Göksal Bilgici
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Matrices Formula for Padovan and Perrin Sequences
, 2013K. Sokhuma, Muban Chom
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Certain Matrices Associated with Balancing and Lucas-balancing Numbers
, 2012P. Ray
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