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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://link.springer.com/article/10.2478%2Fs12175-012-0020-2
Description	The aim of this paper is to give new results about factorizations of the Fibonacci numbers Fn and the Lucas numbers Ln. These numbers are defined by the second order recurrence relation an+2 = an+1+an with the initial terms F0 = 0, F1 = 1 and L0 = 2, L1 = 1, respectively. Proofs of our theorems are done with the help of connections between determinants of tridiagonal matrices and the Fibonacci and the Lucas numbers using the Chebyshev polynomials. Interesting connections were found between the determinants of tridiagonal matrices and the Fibonacci or Lucas numbers. For example, Strang in 1998 presented a family of the n x n tridiagonal matrices, which determinants \|M(n)\| are the Fibonacci numbers F2n+2. Cahill et al. derived a general recurrence for the determinants of a sequence of symmetric tridiagonal matrices and used some sequences of this type for searching of the interesting complex factorizations of the Fibonacci and Lucas numbers. This paper extends the approach used by Cahill in 2004. The aim of this paper is to give new results about factorizations of the Fibonacci numbers Fn and the Lucas numbers Ln. These numbers are defined by the second order recurrence relation an+2 = an+1+an with the initial terms F0 = 0, F1 = 1 and L0 = 2, L1 = 1, respectively. Proofs of our theorems are done with the help of connections between determinants of tridiagonal matrices and the Fibonacci and the Lucas numbers using the Chebyshev polynomials. Interesting connections were found between the determinants of tridiagonal matrices and the Fibonacci or Lucas numbers. For example, Strang in 1998 presented a family of the n x n tridiagonal matrices, which determinants \|M(n)\| are the Fibonacci numbers F2n+2. Cahill et al. derived a general recurrence for the determinants of a sequence of symmetric tridiagonal matrices and used some sequences of this type for searching of the interesting complex factorizations of the Fibonacci and Lucas numbers. This paper extends the approach used by Cahill in 2004. (en)
Title	ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS (en)
skos:prefLabel	ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS (en)
skos:notation	RIV/62690094:18470/12:50000618!RIV13-MSM-18470___
http://linked.open...avai/predkladatel	Přírodovědecká fakulta
http://linked.open...avai/riv/aktivita	S
http://linked.open...avai/riv/aktivity	S
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Seibert, Jaroslav Trojovský, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Hradec Králové / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	156233
http://linked.open...ai/riv/idVysledku	RIV/62690094:18470/12:50000618
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Chebyshev polynomials; tridiagonal matrix; Fibonacci and Lucas numbers (en)
http://linked.open.../riv/klicoveSlovo	tridiagonal matrix Chebyshev polynomials Fibonacci and Lucas numbers
http://linked.open...odStatuVydavatele	SK - Slovenská republika
http://linked.open...ontrolniKodProRIV	[B619659BD6A0]
http://linked.open...i/riv/nazevZdroje	Mathematica Slovaca
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	62
http://linked.open...iv/tvurceVysledku	Seibert, Jaroslav Trojovský, Pavel
http://linked.open...ain/vavai/riv/wos	000303868800007
issn	0139-9918
number of pages	12 (xsd:int)
http://bibframe.org/vocab/doi	10.2478/s12175-012-0020-2
http://localhost/t...ganizacniJednotka	18470
is http://linked.open...avai/riv/vysledek of	ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS

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