2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106081Given $N$ positive integers $a_1, ..., a_N$ with $\gcd(a_1, ..., a_N)=1$, let $f_N$ denote the largest natural number which is not a positive integer combination of $a_1, ..., a_N$. This paper gives an optimal lower bound for $f_N$ in terms of the absolute inhomogeneous minimum of the standard $(N-1)$-simplex.10 pagesNumber Theory11D85; 11H31; 52C17text