A Bound on Solutions of Linear Integer Equalities and Inequalities
Joachim von zur Gathen, Malte Sieveking · Proceedings of the American Mathematical Society · 1978
Consider a system of linear equalities and inequalities with integer coefficients. We describe the set of rational solutions by a finite generating set of solution vectors. The entries of these vectors can be bounded by the absolute value of a certain subdeterminant. The smallest integer solution of the system has coefficients not larger than this subdeterminant times the number of indeterminates. Up to the latter factor, the bound is sharp.