On integers of the forms \(k-2^n\) and \(k2^n+1\)
type: Item
instance of: scholarly article
title: On integers of the forms \(k-2^n\) and \(k2^n+1\)
zbMATH Open document ID: 0992.11012
published in: Journal of Number Theory
publication date: 2002-06-04T00:00:00Z
review text: The author considers the set of odd integers \(k\) such that \(k-2^n\) has at least three distinct prime factors for all positive integers \(n\). He shows that this set contains an infinite arithmetic progression. A similar result is shown for integers of the form \(k2^n+1\). In an earlier result [Proc. Am. Math. Soc. 129, No. 2, 355--361 (2001; Zbl 1010.11004)], the author proved that the set of positive odd integers \(k\) such that \(k2^n+1\) has at least three distinct prime factors for all positive integers \(n\) has positive lower asymptotic density.
reviewed by: N. Saradha
Mathematics Subject Classification ID: 11B25
Mathematics Subject Classification ID: 11A07
zbMATH DE Number: 1749026
zbMATH Keywords: Erdős problems
zbMATH Keywords: congruence covering systems
zbMATH Keywords: infinite arithmetic progression
zbMATH Keywords: distinct prime factors
zbMATH Keywords: positive lower asymptotic density
author: Yonggao Chen
MaRDI profile type: Publication
full work available at URL: jnth.2001.2640
OpenAlex ID: W4213279764
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DOI: 10.1006/JNTH.2001.2640
description: scientific article; zbMATH DE number 1749026