The frobenius problem and its generalizations

Abstract

Let x 1, x 2, ..., x n be positive integers. It is well-known that every sufficiently large integer can be represented as a non-negative integer linear combination of the x i if and only if . The Frobenius problem is the following: given positive integers x 1, x 2, ..., x n with , compute the largest integer not representable as a non-negative integer linear combination of the x i . This largest integer is sometimes denoted g(x 1,..., x n ). © 2008 Springer-Verlag Berlin Heidelberg.