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The Diophantine Frobenius Problem

Jorge L. Ramírez Alfonsín


During the early part of the last century, F. G. Frobenius raised, in his lectures, the following problem (called the Diophantine Frobenius Problem FP): given relatively prime positive integers a1, . . . , an, find the largest natural number (called the Frobenius number and denoted by g(a1, . . . , an)) that is not representable as a nonnegative integer combination of a1, . . . , an. It turned out that the knowledge of g(a1, . . . , an) has been extremely useful to investigate many different problems. A number of methods, from several areas of mathematics, have been used in the hope of finding ... More

Keywords: Frobenius number, denumerants, integer representation, modular change problem, postage stamp problem, semigroups, gaps

Bibliographic Information

Print publication date: 2005 Print ISBN-13: 9780198568209
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780198568209.001.0001


Affiliations are at time of print publication.

Jorge L. Ramírez Alfonsín, author
Maître de Conférences, Université Pierre et Marie Curie, Paris 6