On Divisibility of Fibonomial Coefficients by 3

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F12%3A50000605" target="_blank" >RIV/62690094:18470/12:50000605 - isvavai.cz</a>

Výsledek na webu

<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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Jazyk výsledku

angličtina

Název v původním jazyce

On Divisibility of Fibonomial Coefficients by 3

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

On Divisibility of Fibonomial Coefficients by 3

Popis výsledku anglicky

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.

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

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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

Journal of integer sequences

ISSN

1530-7638

e-ISSN

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Svazek periodika

15

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

10

Strana od-do

1-10

Kód UT WoS článku

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EID výsledku v databázi Scopus

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