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## On Frobenius numbers in three variables

##### Date

2006-08-15##### Author

Trimm, Janet

##### Type of Degree

Dissertation##### Department

Mathematics and Statistics##### Metadata

Show full item record##### Abstract

Given a set of relatively prime positive integers
$\{a_1,a_2,\ldots, a_n\}$, after some point all positive integers are representable as a linear combination of the set with nonnegative coefficients. Which integer is the last one not so
representable is the Frobenius problem, or the Frobenius stamp problem, and the number in question the Frobenius number of the set. While the two-variable solution is widely known, and the
general solution is NP-hard, there have been several algorithmic solutions of the three-variable problem. Here we present a new bound for the Frobenius number of most relatively prime triples.