Proof of a conjecture by Erdős and Graham concerning the problem of Frobenius
type: Item
instance of: scholarly article
title: Proof of a conjecture by Erdős and Graham concerning the problem of Frobenius
zbMATH Open document ID: 0695.10012
DOI: 10.1016/0022-314X(90)90150-P
author: Jacques Dixmier
published in: Journal of Number Theory
publication date: 1990-01-01T00:00:00Z
review text: Let \(x_ 1<x_ 2<...<x_ b\) be integers with \(g.c.d.(x_ 1,...,x_ b)=1\), \(G(x_ 1,...,x_ b)\) the Frobenius number of this system of integers and \(g(b,a)=\sup G(x_ 1,...,x_ b)\) where the upper bound is taken over all such systems with \(x_ b=a\). It is proved that g(b,a) is roughly equal to \(a^ 2/(b-1)\) and the exact value of g(b,a) is given if \(b-1\) divides a or \(a-1\) or \(a-2.\)
Mathematics Subject Classification ID: 11D04
zbMATH DE Number: 4137861
zbMATH Keywords: Frobenius problem
zbMATH Keywords: linear diophantine equation
zbMATH Keywords: Frobenius number
reviewed by: Joachim Piehler
MaRDI profile type: Publication
Wikidata QID: Q123328324
cites work: On a Problem of Partitions
cites work: On a linear diophantine problem of Frobenius
cites work: Q3872528
cites work: Q5515488
cites work: A Bound for a Solution of a Linear Diophantine Problem
cites work: Bounds for a Linear Diophantine Problem of Frobenius, II
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description: scientific article; zbMATH DE number 4137861