Some experimental results on the Frobenius problem

Details Some experimental results on the Frobenius problem Some experimental results on the Frobenius problem

2002-04-02

arxiv.org/abs/math/0204036v3

Experimental Mathematics 12, no. 3 (2003), 263-269

Mathematics

Number Theory

10 pages, 3 figures

Scientific paper

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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