ON THE LINEAR DIOPHANTINE PROBLEM OF FROBENIUS

被引：37

作者：

DAVISON, JL ^{[1
]}

机构：

[1] LAURENTIAN UNIV,DEPT MATH & COMP SCI,SUDBURY P3E 2C6,ONTARIO,CANADA

来源：

JOURNAL OF NUMBER THEORY | 1994年 / 48卷 / 03期

关键词：

D O I：

10.1006/jnth.1994.1071

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose a, b, c are three positive integers with gcd = 1. We consider the function f(a, b, c) defined to be the largest integer not representable as a positive integral linear combination of a, b, c. We give a new lower bound for f(a, b, c) which is shown to be tight, and we give a new proof of a theorem due to Vitek on an upper bound. A polynomial time algorithm, based on modifications to Rodseth and Selmer/Beyer algorithms, is given for the computation of f(a, b, c). Finally, some open problems are discussed. (C) 1994 Academic Press, Inc.

引用

页码：353 / 363

页数：11