An application of an optimal behaviour of the greedy solution in number theory

Let a1, a2, ..., an be relative prime positive integers. The Frobenius problem is to determine the greatest integer not belonging to the set {Σj=1 najxj :x∈Z+ n}. The Frobenius problem belongs to the combinatorial number theory, which is very rich in methods. In this paper the Frobenius problem is handled by integer programming which is a new tool in this field. Some new upper bounds and exact solutions of subproblems are provided. A lot of earlier results obtained with very different methods can be discussed in a unified way.