Some experimental results on the Frobenius problem

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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 $\sqrt{a_1 a_2 a_3}^{5/4} - a_1 - a_2 - a_3$.
10 pages, 3 figures

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Number Theory, Combinatorics, 05A15, 11P21; 11Y16

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http://salesiana.dossiersoluciones.com/handle/123456789/63704

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0204036
 http://arxiv.org/abs/math/0204036
 Experimental Mathematics 12, no. 3 (2003), 263-269

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arXiv