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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

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.

Frobenius, coin-exchange, linear Diophantine system
Mathematical Subject Classification 2010
Primary: 11B75, 11D04, 11D72
Received: 2 March 2011
Revised: 9 May 2011
Accepted: 9 May 2011
Published: 17 January 2012

Communicated by Scott Chapman
Jeffrey Amos
Department of Mathematics
Kansas State University
Manhattan, KS 66506
United States
Iuliana Pascu
Department of Economics
Massachusetts Institute of Technology
50 Memorial Drive
Cambridge, MA 02142
United States
Vadim Ponomarenko
Department of Mathematics and Statistics
San Diego State University
5500 Campanile Drive
San Diego CA 92182-7720
United States
Enrique Treviño
Department of Mathematics
Dartmouth College
Hanover, NH 03755
United States
Yan Zhang
Department of Mathematics
Massachusetts Institute of Technology
50 Memorial Drive
77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States