The Pell and Pell-Lucas Numbers via Square Roots of Matrices

Saadet Arslan, Fikri Köken

Abstract


In this paper, the Pell and Pell-Lucas numbers with specialized rational subscripts are derived from general expressions by square roots of the matrices \(M^n\) and \(N^n\). Besides, we reveal that the identities involving these numbers are produced by square roots of matrices \(M^{n/2}\) and \(N^{n/2}\). Further we show that the matrices \(M^n\) and \(N^n\) are generalized to rational powers by using the Abel's functional equation.

Keywords


Pell and Pell-Lucas Numbers, Square Roots of Matrices

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v8i3.393

eISSN 0975-5748; pISSN 0974-875X