ON DIVISIBILITY PROPERTIES OF CERTAIN FIBONOMIAL COEFFICIENTS BY A PRIME

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F13%3A50001529" target="_blank" >RIV/62690094:18470/13:50001529 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

ON DIVISIBILITY PROPERTIES OF CERTAIN FIBONOMIAL COEFFICIENTS BY A PRIME

Popis výsledku v původním jazyce

Let (F_n) be the Fibonacci sequence given by the recurrence relation F_(n+2) = F_(n+1) +F_n, with F_0 = 0 and F_1 = 1. These numbers are well-known for possessing amazing properties. Fonten´e generalized binomial coefficients [n, k], replacing the natural numbers by the terms of an arbitrary sequence (A_n) of real or complex numbers. Since 1960, there has been much interest in the Fibonomial coefficients [n,k]_F which correspond to the choice A_n = F_n. In recent papers, Marques and Trojovsky proved that p | [p^(a+1),p^a]_F holds for all positive integers a and primes p=2, p=3. In this paper, we are interested in studying such Fibonomial coefficient divisibility properties for other prime numbers. Although such divisibilities are not true for all primes (e.g., 11not| [11^2,11]_F ), we desire to search for a large class of them. We show that this property holds for all primes in the form p equiv -2,2 (mod 5).

Název v anglickém jazyce

ON DIVISIBILITY PROPERTIES OF CERTAIN FIBONOMIAL COEFFICIENTS BY A PRIME

Popis výsledku anglicky

Let (F_n) be the Fibonacci sequence given by the recurrence relation F_(n+2) = F_(n+1) +F_n, with F_0 = 0 and F_1 = 1. These numbers are well-known for possessing amazing properties. Fonten´e generalized binomial coefficients [n, k], replacing the natural numbers by the terms of an arbitrary sequence (A_n) of real or complex numbers. Since 1960, there has been much interest in the Fibonomial coefficients [n,k]_F which correspond to the choice A_n = F_n. In recent papers, Marques and Trojovsky proved that p | [p^(a+1),p^a]_F holds for all positive integers a and primes p=2, p=3. In this paper, we are interested in studying such Fibonomial coefficient divisibility properties for other prime numbers. Although such divisibilities are not true for all primes (e.g., 11not| [11^2,11]_F ), we desire to search for a large class of them. We show that this property holds for all primes in the form p equiv -2,2 (mod 5).

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

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Fibonacci quarterly

ISSN

0015-0517

e-ISSN

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Svazek periodika

51

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

6

Strana od-do

78-83

Kód UT WoS článku

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EID výsledku v databázi Scopus

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