On two conjectures about practical numbers
type: Item
instance of: scholarly article
title: On two conjectures about practical numbers
zbMATH Open document ID: 0848.11002
author: Giuseppe Melfi
published in: Journal of Number Theory
publication date: 1996-03-19T00:00:00Z
review text: It has been conjectured by \textit{M. Margenstern} [J. Number Theory 37, 1-36 (1991; Zbl 0715.11001)] that every positive even integer is a sum of two practical numbers and there are infinitely many triples \(m- 2\), \(m\), \(m+ 2\) of practical numbers. (A number \(m\) is practical if every integer in the interval \([1, \sigma(m)]\) is a sum of distinct positive divisors of \(m\).) The author establishes these conjectures using a characterization of practical numbers due to \textit{B. M. Stewart} [Am. J. Math. 76, 779-785 (1954; Zbl 0056.27004)].
Mathematics Subject Classification ID: 11A25
zbMATH DE Number: 844647
zbMATH Keywords: sum of practical numbers
zbMATH Keywords: triples of practical numbers
reviewed by: Władysław Narkiewicz
MaRDI profile type: Publication
full work available at URL: jnth.1996.0012
OpenAlex ID: W2095384851
Wikidata QID: Q55880187
DOI: 10.1006/JNTH.1996.0012
description: scientific article; zbMATH DE number 844647