ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
ON FACTORIZATION OF THE FIBONACCI AND LUCAS NUMBERS USING TRIDIAGONAL DETERMINANTS
Original language 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
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Mathematica Slovaca
ISSN
0139-9918
e-ISSN
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Volume of the periodical
62
Issue of the periodical within the volume
3
Country of publishing house
SK - SLOVAKIA
Number of pages
12
Pages from-to
439-450
UT code for WoS article
000303868800007
EID of the result in the Scopus database
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