On a linear diophantine problem for geometrical type sequences
type: Item
instance of: scholarly article
title: On a linear diophantine problem for geometrical type sequences
zbMATH Open document ID: 0615.10021
DOI: 10.1016/0012-365X(87)90116-6
author: Endre Boros
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let \(A=\{a_ 0,a_ 1,...,a_ n\}\) be a set of relatively prime positive integers, g(A) the Frobenius number, i.e. the greatest b for which \(b=\sum^{n}_{i=0}a_ ix_ i\) has no solution in nonnegative integers \(x_ i\), and n(A) the number of all positive b for which there is no such solution. In this paper the author gives the exact values of g(A) and n(A) in the case where the set A forms an almost geometric progression \(a_ j=h_ ja_ 0+\prod^{j-1}_{i=0}q_ i\) for \(j=1,...,n\), \(g.c.d.(a_ 0,q_ 0)=0\) with \(a_ 0\), \(h_ j\), \(q_{j-1}\), \(j=1,...,n\) given positive integers.
Mathematics Subject Classification ID: 11D04
Mathematics Subject Classification ID: 90C10
zbMATH DE Number: 3995770
zbMATH Keywords: linear diophantine equation
zbMATH Keywords: Frobenius problem
zbMATH Keywords: Frobenius number
zbMATH Keywords: almost geometric progression
Wikidata QID: Q59561146
reviewed by: Joachim Piehler
MaRDI profile type: Publication
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full work available at URL: 0012-365x(87)90116-6
OpenAlex ID: W2002372178
DBLP publication ID: journals/dm/Boros87
description: scientific article; zbMATH DE number 3995770