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29 March 2024
 
  » arxiv » math.NT/0204036

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Some experimental results on the Frobenius problem
Matthias Beck ; David Einstein ; Shelemyahu Zacks ;
Date 2 Apr 2002
Journal Experimental Mathematics 12, no. 3 (2003), 263-269
Subject Number Theory; Combinatorics MSC-class: 05A15, 11P21; 11Y16 | math.NT math.CO
AbstractWe study the Frobenius problem: given relatively prime positive integers $a_1,...,a_d$, find the largest value of t (the Frobenius number) such that $sum_{k=1}^d m_k a_k = t$ has no solution in nonnegative integers $m_1,...,m_d$. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by $sqrt{a_1 a_2 a_3}^{5/4} - a_1 - a_2 - a_3$.
Source arXiv, math.NT/0204036
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