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2003 Some Experimental Results on the Frobenius Problem
Matthias Beck, David Einstein, Shelemyahu Zacks
Experiment. Math. 12(3): 263-270 (2003).

Abstract

We study the Frobenius problem: Given relatively prime positive integers {\small $a_{1} , \dots , a_{d}$}, find the largest value of {\small $t$} (the Frobenius number) such that {\small $ \sum_{k=1}^d m_{k} a_{k} = t $} has no solution in nonnegative integers {\small $ m_{ 1 } , \dots , m_{ d } $}. Based on empirical data, we conjecture that except for some special cases, the Frobenius number can be bounded from above by {\small $ \sqrt{a_{1}a_{2}a_{3}}^{5/4} - a_1 - a_2 - a_3 $}.

Citation

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Matthias Beck. David Einstein. Shelemyahu Zacks. "Some Experimental Results on the Frobenius Problem." Experiment. Math. 12 (3) 263 - 270, 2003.

Information

Published: 2003
First available in Project Euclid: 15 June 2004

zbMATH: 1076.11015
MathSciNet: MR2034391

Subjects:
Primary: 05A15, 11Y16
Secondary: 11P21

Rights: Copyright © 2003 A K Peters, Ltd.

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Vol.12 • No. 3 • 2003
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