An Optimal Lower Bound for the Frobenius Problem

Details An Optimal Lower Bound for the Frobenius Problem An Optimal Lower Bound for the Frobenius Problem

2005-12-05

arxiv.org/abs/math/0512083v4

Mathematics

Number Theory

10 pages

Scientific paper

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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