Arithmetical properties of a sequence arising from an arctangent sum
type: Item
instance of: scholarly article
title: Arithmetical properties of a sequence arising from an arctangent sum
zbMATH Open document ID: 1149.11007
author: T. Amdeberhan
author: Luis Medina
author: Victor H. Moll
published in: Journal of Number Theory
publication date: 2008-06-09T00:00:00Z
review text: The authors study the sequence \(x_n=(n+x_{n-1})/(1-nx_{n-1})\) with \(x_1=1\), which appeared in the context of arctangent sums. The authors prove that \(x_n \neq 0\) for \(n \geq 4\), and conjecture that \(x_n\) is not an integer for \(n \geq 5\). The authors also conjecture that \(\prod_{i=1}^n (i^2+1)\) is not a square, for \(n \geq 3\) , and give partial results. This has meanwhile been proved by \textit{J. Cilleruelo} [J. Number Theory 128, No. 8, 2488--2491 (2008; Zbl 1213.11057)].
reviewed by: Christian Elsholtz
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 11B83
Mathematics Subject Classification ID: 11A07
Mathematics Subject Classification ID: 11A51
Mathematics Subject Classification ID: 11N32
zbMATH DE Number: 5285748
zbMATH Keywords: arctangent sum
zbMATH Keywords: recurrent sequence
MaRDI profile type: Publication
full work available at URL: j.jnt.2007.05.008
OpenAlex ID: W2028218333
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DOI: 10.1016/J.JNT.2007.05.008
description: scientific article; zbMATH DE number 5285748