Abstract
Leta 1,a 2, ...,a n be relative prime positive integers. The Frobenius problem is to determine the greatest integer not belonging to the set {Σ n j=1 a j x j :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.
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Vizvári, B. An application of an optimal behaviour of the greedy solution in number theory. Period Math Hung 27, 69–83 (1993). https://doi.org/10.1007/BF01876632
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DOI: https://doi.org/10.1007/BF01876632