Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 1, pp. 49-55 (2000)

On Minimal Solutions of Diophantine Equations

Martin Henk, Robert Weismantel

Fachbereich Mathematik, IMO, Otto-von Guericke-Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany e-mail: henk@imo.mathematik.uni-magdeburg.de e-mail: weismantel@imo.mathematik.uni-magdeburg.de

Abstract: This paper investigates the region in which all the minimal solutions of a linear diophantine equation lie. We present best possible inequalities which must be satisfied by these solutions and thereby improve earlier results.

Keywords: linear Diophantine equations, Hilbert basis, pointed rational cones.

Classification (MSC2000): 51A30, 51B05

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