Products of Fibonacci numbers with indices in an interval and at most four omitted being a power
type: Item
instance of: scholarly article
title: Products of Fibonacci numbers with indices in an interval and at most four omitted being a power
zbMATH Open document ID: 1219.11031
DOI: 10.1016/S0019-3577(09)80025-6
author: Florian Luca
author: T. N. Shorey
published in: Indagationes Mathematicae. New Series
publication date: 2011-03-31T00:00:00Z
review text: Let \((F_n)_{n\geq 0}\) be the Fibonacci numbers. Let \(n\geq 1\), \(k\geq 5\) and \({\mathcal I}\subseteq\{n,n+1,\dots,n+k-1\} \) such that \(|{\mathcal I}|\geq k-4\) and \[ \prod_{i\in{\mathcal I} }F_i=y^m \] holds with some integers \(y\) and \(m\geq 2\). The authors prove that \[ {\mathcal I}\in \{\{1\},\{2\},\{6\},\{12\},\{1,2\},\{1,6\},\{2,6\},\{3,6\},\{1,2,6\},\{1,3,6\},\{2,3,6\},\{1,2,3,6\}\}. \]
reviewed by: Florin Nicolae
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 5872498
zbMATH Keywords: Fibonacci numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5872498