2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63704We 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 figuresNumber TheoryCombinatorics05A15, 11P21; 11Y16text