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Some experimental results on the Frobenius problem

Matthias Beck·David Einstein·Shelemyahu Zacks
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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 $\sqrt{a_1 a_2 a_3}^{5/4} - a_1 - a_2 - a_3$.

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Matthias Beck, David Einstein, Shelemyahu Zacks. 2005-01-02. Some experimental results on the Frobenius problem. https://arxiv.org/abs/math/0204036

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