{"title":"WEIGHTED SYLVESTER SUMS ON THE FROBENIUS SET IN MORE VARIABLES","authors":"T. Komatsu, Yuan Zhang","doi":"10.2206/kyushujm.76.163","DOIUrl":null,"url":null,"abstract":"Given positive integers a1, . . . , ak with gcd(a1, . . . , ak) = 1, it is well-known that all sufficiently large n can be represented as a nonnegative integer combination of a1, . . . , ak. The Frobenius Problem is to determine the largest positive integer that is NOT representable as a nonnegative integer combination of given positive integers that are coprime (see [15] for general references). This number is denoted by g(a1, . . . , ak) and often called Frobenius number. The Frobenius Problem has been also known as the Coin Exchange Problem (or Postage Stamp Problem / Chicken McNugget Problem), which","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2021-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/kyushujm.76.163","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 16
Abstract
Given positive integers a1, . . . , ak with gcd(a1, . . . , ak) = 1, it is well-known that all sufficiently large n can be represented as a nonnegative integer combination of a1, . . . , ak. The Frobenius Problem is to determine the largest positive integer that is NOT representable as a nonnegative integer combination of given positive integers that are coprime (see [15] for general references). This number is denoted by g(a1, . . . , ak) and often called Frobenius number. The Frobenius Problem has been also known as the Coin Exchange Problem (or Postage Stamp Problem / Chicken McNugget Problem), which
期刊介绍：
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.
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