ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F12%3A50000618" target="_blank" >RIV/62690094:18470/12:50000618 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/article/10.2478%2Fs12175-012-0020-2" target="_blank" >http://link.springer.com/article/10.2478%2Fs12175-012-0020-2</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2478/s12175-012-0020-2" target="_blank" >10.2478/s12175-012-0020-2</a>

Jazyk výsledku

angličtina

Název v původním jazyce

ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2012

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Mathematica Slovaca

ISSN

0139-9918

e-ISSN

—

Svazek periodika

62

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

SK - Slovenská republika

Počet stran výsledku

12

Strana od-do

439-450

Kód UT WoS článku

000303868800007

EID výsledku v databázi Scopus

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