Some Experimental Results on the Frobenius Problem
Beck, Matthias ; Einstein, David ; Zacks, Shelemyahu
Experiment. Math., Tome 12 (2003) no. 1, p. 263-270 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 $}.
Publié le : 2003-05-14
Classification:  The linear Diophantine problem of Frobenius,  upper bounds,  algorithms,  05A15,  11Y16,  11P21 
@article{1087329230,
     author = {Beck, Matthias and Einstein, David and Zacks, Shelemyahu},
     title = {Some Experimental Results on the Frobenius Problem},
     journal = {Experiment. Math.},
     volume = {12},
     number = {1},
     year = {2003},
     pages = { 263-270},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1087329230}
}

Beck, Matthias; Einstein, David; Zacks, Shelemyahu. Some Experimental Results on the Frobenius Problem. Experiment. Math., Tome 12 (2003) no. 1, pp.  263-270. http://gdmltest.u-ga.fr/item/1087329230/