On Divisibility of Fibonomial Coefficients by 3

Result code in IS VaVaI
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Result on the web
<a href="https://cs.uwaterloo.ca/journals/JIS/VOL15/Trojovsky/trojovsky2.pdf" target="_blank" >https://cs.uwaterloo.ca/journals/JIS/VOL15/Trojovsky/trojovsky2.pdf</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
On Divisibility of Fibonomial Coefficients by 3
Original language description
Let (Fn) be the Fibonacci sequence given by the recurrence relation Fn+2=Fn+1+Fn, with F0=0 and F1=1. These numbers are well-known for possessing amazing properties. Since 1964, there has been an accelerated interest in the Fibonomial coefficients [m,k]F, which are a generalization of binomial coefficients. The Fibonomial coefficients arise by replacing the natural numbers by the terms of sequence (Fn). Several authors became interested in the divisibility properties of binomial coefficients. In a veryrecent paper we proved, among other things, that 2 divides [2n,n] F for all integers n > 1. In this paper, we shall study similar problems for the Fibonomial coefficients. We will find a necessary and sufficient condition for that 3 divides [3n,n]F. Further we shall deal with the divisibility of [sn,n]F by 3 for some positive integers n and s.
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
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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