A new reduction method in integer programming (Q1115800)

Let \(a_ 1^ Tx=b_ 1\) and \(a_ 2^ T=b_ 2\) be two equations in nonnegative integer unkowns \(x_ 1,...,x_ n\), where \(a\in {\mathbb{Z}}^ n_+\) and \(b\in {\mathbb{Z}}_+\). The equation \[ (t_ 1a_ 1+t_ 2a_ 2)^ Tx=t_ 1b_ 1+t_ 2b_ 2 \] has the some solutions as the system of the 2 initial equations, provided \(t_ 1\) and \(t_ 2\) are suitably chosen. A single inequality constraint is presented that gives such values for \(t_ 1\) and \(t_ 2\).