The proof of a generalization of Borosh-Treybig's hypothesis for Diophantine equations (Q2729350)

The author studies nonnegative solutions of linear Diophantine equations of the form \(Ax = a\) on a nonhomogeneous lattice \(L\). As a result, it is proven that there exists a nonnegative solution \(x^0\) to the equation such that, for the components of the solution, the inequalities \(x_i^0 \leq dl\), \(i\in\mathbb N\), hold, where \(l = \det L\) and \(d\) is a maximal minor of a matrix with order equal to \(\operatorname{rank} A\).NEWLINENEWLINENEWLINEBorosh-Treybig's hypothesis corresponds to the case \(l = 1\).