On three questions concerning \(0,1\)-polynomials
type: Item
instance of: scholarly article
title: On three questions concerning \(0,1\)-polynomials
zbMATH Open document ID: 1136.11020
author: Michael Filaseta
author: Carrie Finch
author: Charles Nicol
published in: Journal de Théorie des Nombres de Bordeaux
publication date: 2007-03-20T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10759
review text: The three main results proved in this paper are the following: 1) For every integer \(n\geq36\) the polynomial \( X^n+ X^{35}+ X^{34}+ X^{33}+ X^{32}+ X^{16}+ X^{15}+ X^{3}+1 \) is irreducible over the integers. 2) If \(a<b<c\) are positive integers then at least one of the polynomials \(X^b+X^a+1\), \(X^c+ X^b+1\) and \(X^c+X^a +1\) is irreducible over the integers. 3) There exists an infinite set of positive integers \(S\) such that if \(\{e_1,\ldots, e_n \}\) is any finite subset of \(S\) then the polynomial \( X^{e_1}+X^{e_2}+\cdots+X^{e_n}+1 \) is irreducible over the integers.
Mathematics Subject Classification ID: 11C08
zbMATH DE Number: 5135395
zbMATH Keywords: 0,1-polynomials
reviewed by: Maurice Mignotte
MaRDI profile type: Publication
OpenAlex ID: W1964667438
cites work: Q4252157
cites work: On an irreducibility theorem of A. Schinzel associated with coverings of the integers
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DOI: 10.5802/JTNB.549
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description: scientific article; zbMATH DE number 5135395