Some experimental results on the Frobenius problem

2002/04/30 by Matthias Beck, David Einstein, Shelemyahu Zacks
Mathematics · #math.NT #math.CO #msc:05A15 #msc:11P21 #msc:11Y16

paper · pdf

published as Experimental Mathematics 12, no. 3 (2003), 263-269 · 10 pages, 3 figures

arxiv created 2005/01/02 · arxiv updated 2009/11/30

Abstract

We study the Frobenius problem: given relatively prime positive integers a₁,...,a_d, find the largest value of t (the Frobenius number) such that ∑_k=1^d m_k a_k = t has no solution in nonnegative integers m₁,...,m_d. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by √(a₁ a₂ a₃)^5/4 - a₁ - a₂ - a₃.

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