#### Vol. 4, No. 2, 2011

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The multidimensional Frobenius problem

### Jeffrey Amos, Iuliana Pascu, Vadim Ponomarenko, Enrique Treviño and Yan Zhang

Vol. 4 (2011), No. 2, 187–197
##### Abstract

We provide a variety of results concerning the problem of determining maximal vectors $g$ such that the Diophantine system $Mx=g$ has no solution: conditions for the existence of $g$, conditions for the uniqueness of $g$, bounds on $g$, determining $g$ explicitly in several important special cases, constructions for $g$, and a reduction for $M$.

##### Keywords
Frobenius, coin-exchange, linear Diophantine system
##### Mathematical Subject Classification 2010
Primary: 11B75, 11D04, 11D72