Sequential and simultaneous aggregation of diophantine equations

For any system of linear algebraic equations with integer coefficients and a bounded set of nonnegative integer solutions, an infinite number of equations exist, each of which has the same set of nonnegative integer solutions as the given system. Two approaches (sequential and simultaneous aggregation) to the problem of finding the latter equivalent equation are considered. New procedures for sequential and simultaneous aggregation are presented, which improve known results, i.e., provide equivalent equations with smaller coefficients.