Lattice translates of a polytope and the Frobenius problem (Q1196686)

Given \(n\) coprime natural numbers \(a_ 1,a_ 2,\ldots,a_ n\) the Frobenius problem of finding the largest natural number not expressible as \(a_ 1x_ 1+a_ 2x_ 2+\cdots+a_ nx_ n\) with nonnegative \(x_ 1,x_ 2,\ldots,x_ n\) is an \(NP\)-hard problem. By using some recent results in the Geometry of Numbers a polynomial time algorithm for every fixed \(n\) is given.