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On integers nonrepresentable by a generalized arithmetic progression. (English) Zbl 1139.11301
Summary: We consider those positive integers that are not representable as linear combinations of terms of a generalized arithmetic progression with nonnegative integer coefficients. To do this, we make use of the numerical semigroup generated by a generalized arithmetic progression. The number of integers nonrepresentable by such a numerical semigroup is determined as well as that of its dual. In addition, we find the number and the sum of those integers representable by the dual of the semigroup that are not representable by the semigroup itself.

MSC:
11B25 Arithmetic progressions
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