On divisibility properties of certain fibonomial coefficients by a prime

Diego Marques; James A. Sellers; Pavel Trojovský

On divisibility properties of certain fibonomial coefficients by a prime

Diego Marques, James A. Sellers, Pavel Trojovský

Research output: Contribution to journal › Article › peer-review

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
State	Published - Feb 2013
Externally published	Yes

OpenUrl availability

Full text

Cite this

@article{4abb61d47d844396acdfa32c8607ede2,

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,

language = "English (US)",

volume = "51",

pages = "78--83",

journal = "Fibonacci Quarterly",

issn = "0015-0517",

publisher = "Fibonacci Association",

number = "1",

}

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=84874897604&partnerID=8YFLogxK

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

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

Abstract

OpenUrl availability

Other files and links

Fingerprint

Cite this