On divisibility properties of certain fibonomial coefficients by a prime

Diego Marques; James A. Sellers; Pavel Trojovský

doi:10.1080/00150517.2013.12427974

On divisibility properties of certain fibonomial coefficients by a prime

Diego Marques, James A. Sellers, Pavel Trojovský

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9 Scopus citations

Abstract

Let (F_n)_n≥o be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as {equation presented}, for k > m. In this paper, we shall prove that if p is a prime number such that p ≡ -2 or 2 (mod 5), then p | {equation presented} for all a ≥ 1.

Original language	English (US)
Pages (from-to)	78-83
Number of pages	6
Journal	Fibonacci Quarterly
Volume	51
Issue number	1
DOIs	https://doi.org/10.1080/00150517.2013.12427974
State	Published - Feb 2013
Externally published	Yes

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title = "On divisibility properties of certain fibonomial coefficients by a prime",

abstract = "Let (Fn)n≥o be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as \{equation presented\}, for k > m. In this paper, we shall prove that if p is a prime number such that p ≡ -2 or 2 (mod 5), then p | \{equation presented\} for all a ≥ 1.",

author = "Diego Marques and Sellers, \{James A.\} and Pavel Trojovsk{\'y}",

year = "2013",

month = feb,

doi = "10.1080/00150517.2013.12427974",

language = "English (US)",

volume = "51",

pages = "78--83",

journal = "Fibonacci Quarterly",

issn = "0015-0517",

publisher = "Fibonacci Association",

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T1 - On divisibility properties of certain fibonomial coefficients by a prime

AU - Marques, Diego

AU - Sellers, James A.

AU - Trojovský, Pavel

PY - 2013/2

Y1 - 2013/2

N2 - Let (Fn)n≥o be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as {equation presented}, for k > m. In this paper, we shall prove that if p is a prime number such that p ≡ -2 or 2 (mod 5), then p | {equation presented} for all a ≥ 1.

AB - Let (Fn)n≥o be the Fibonacci sequence. For 1 ≤ k ≤ m, the Fibonomial coefficient is defined as {equation presented}, for k > m. In this paper, we shall prove that if p is a prime number such that p ≡ -2 or 2 (mod 5), then p | {equation presented} for all a ≥ 1.

UR - https://www.scopus.com/pages/publications/84874897604

UR - https://www.scopus.com/inward/citedby.url?scp=84874897604&partnerID=8YFLogxK

U2 - 10.1080/00150517.2013.12427974

DO - 10.1080/00150517.2013.12427974

M3 - Article

AN - SCOPUS:84874897604

SN - 0015-0517

VL - 51

SP - 78

EP - 83

JO - Fibonacci Quarterly

JF - Fibonacci Quarterly

IS - 1

ER -

On divisibility properties of certain fibonomial coefficients by a prime

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