**Author(s): ** Gilberto Garcia Pulgarín |

John Hermes Castillo Gómez |

Wilson Fernando Mutis Cantero |

Fernando Andrés Benavides Agredo**Journal: ** Revista Sigma ISSN 2027-064X

**Volume: ** X;

**Start page: ** 18;

**Date: ** 2010;

VIEW PDF DOWNLOAD PDF Original page**Keywords: ** Postage Stamp Problem |

Additive bases**ABSTRACT**

Let h a positive integer, A a set of positive integers, with hA we denote the set of all integers representable as a sum of at most h elements of A (allowing repetitions). The Postage Stamp Problem, is to find the largest integer n = n(h,A) such that {1, . . . , n} hA.In this paper we present a new proof of the result of St¨ohr that say how to calculate n(h,A) when A has two elements. From this result we show that if h is a positive integer there exists a set A which is an extremal (, h)−basis and an extremal (, h+ 1)−basis for two stamps.In addition, we find the cases when exist a set which is an extremal (, h)−basis and an extremal (, h + 1)−basis in the case of three stamps.

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