ON THE SUM OF POWERS OF TWO k-FIBONACCI NUMBERS WHICH BELONGS TO THE SEQUENCE OF k-LUCAS NUMBERS

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F16%3A50005614" target="_blank" >RIV/62690094:18470/16:50005614 - isvavai.cz</a>
Result on the web
<a href="https://www.degruyter.com/downloadpdf/j/tmmp.2016.67.issue-1/tmmp-2016-0028/tmmp-2016-0028.pdf" target="_blank" >https://www.degruyter.com/downloadpdf/j/tmmp.2016.67.issue-1/tmmp-2016-0028/tmmp-2016-0028.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/tmmp-2016-0028" target="_blank" >10.1515/tmmp-2016-0028</a>

Result language
angličtina
Original language name
ON THE SUM OF POWERS OF TWO k-FIBONACCI NUMBERS WHICH BELONGS TO THE SEQUENCE OF k-LUCAS NUMBERS
Original language description
Let k>0 and denote (F{k,n}){n>-1}, the k-Fibonacci sequence whose terms satisfy the recurrence relation F{k,n}=kF{k,n-1}+F{k,n-2}, with initial conditions F{k,0}=0 and F{k,1}=1. In the same way, the k-Lucas sequence (L{k,n}){n>-1} is defined by satisfying the same recurrence relation with initial values L{k,0}=2 and L{k,1}=k. These sequences was introduced by Falcon and Plaza and they showed many of its properties too. In particular, they proved that F{k,n+1}+F_k,n-1}=L{k,n}, for all k>0 and n>-1. In this paper, we shall prove that if k>0 and F{k,n+1}^s+F_{k,n-1}^s belongs to (L{k,m}){m>0} for infinitely many positive integers n, then s=1.
Czech name
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Czech description
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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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Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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