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An Optimal Lower Bound for the Frobenius Problem

Iskander Aliev·Peter Gruber
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Abstract

Given $N$ 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.

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Iskander Aliev, Peter Gruber. 2006-03-29. An Optimal Lower Bound for the Frobenius Problem. https://arxiv.org/abs/math/0512083

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