Some experimental results on the Frobenius problem

Matthias Beck; David Einstein; Shelemyahu Zacks

Some experimental results on the Frobenius problem

Number Theory 2007-05-23 v3 Combinatorics

Authors: Matthias Beck , David Einstein , Shelemyahu Zacks

Abstract

We 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 $\sqrt{a_1 a_2 a_3}^{5/4} - a_1 - a_2 - a_3$ .

Keywords

number theory divisor function

Cite

@article{arxiv.math/0204036,
  title  = {Some experimental results on the Frobenius problem},
  author = {Matthias Beck and David Einstein and Shelemyahu Zacks},
  journal= {arXiv preprint arXiv:math/0204036},
  year   = {2007}
}

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10 pages, 3 figures

Some experimental results on the Frobenius problem

Abstract

Keywords

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