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

Mathematics

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

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
State	Published - Feb 2013

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

Cite this

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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}",

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language = "English (US)",

volume = "51",

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journal = "Fibonacci Quarterly",

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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

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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.

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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

All Science Journal Classification (ASJC) codes

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