Given a set of linear Diophantine Equations (LDE's), where each equation is one of the following form:
Let be a positive integer constant. Also, the number of variables in each equation is exactly .
For every such set of LDE problem instance, the problem is solvable iff, at least one such solution exists, such that each variable's assigned value in that solution is:
In other words, the solution if it exists is bounded by the constant and 0.
Can someone help with the proof of the above statement (or counterexamples with some small )?