I am following 'Application of Number Theory to Numerical Analysis', and there is a section by G.H. Bradley called 'Modulo Optimization Problems and Integer Linear Programming'. There he explains that turns a modulo integer programming problem into an equivalent integer programming problem.
However, I can't follow one part. Given a modulo integer program $Ax=b \mod k$, we usually turn it into $Ax + Ky = b$, and thus from $m$ equations, $n$ variables we get $m$ equations, $m+n$ variables. He then outlines a procedure so that we only have $n$ variables instead of $m+n$, and this part is a bit unclear to me.
I don't necessarily have to follow Bradley's section, but I do not know much (yet) about operations research books. I would like to ask if someone knows an easier to read book/article where I can find this elimination of variables procedure.
Edit: I misquoted the number of variables and constraint change. It is from $m$ constraints and $n+m$ variables into $n$ variables $n$ constraints. Still very good in some cases.