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Unbounded Discrepancy in Frobenius Numbers

Jeffrey Shallit / James Stankewicz
Published Online: 2011-02-24 | DOI: https://doi.org/10.1515/integ.2011.002


Let gj denote the largest integer that is represented exactly j times as a non-negative integer linear combination of {x 1, . . . , xn }. We show that for any k > 0, and n = 5, the quantity g 0gk is unbounded. Furthermore, we provide examples with g 0 > gk for n ≥ 6 and g 0 > g 1 for n ≥ 4.

Keywords.: Discrepancy; Frobenius number; generalized Frobenius number; linear Diophantine equation

About the article

Received: 2010-02-25

Revised: 2010-09-09

Accepted: 2010-09-16

Published Online: 2011-02-24

Published in Print: 2011-02-01

Citation Information: Integers, Volume 11, Issue 1, Pages 27–34, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2011.002.

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