# Computational Complexity of Integer Linear Program [with Fixed number of 'Pure Constants']

This is a follow up to the previous Question: Conditions for Linear Diophantine Equations to always have a solution

It was established in the above's answer that obtaining or testing for the existence of an solution of an ILP in $\mathbb N$ is an NP Hard Problem. This in turn makes obtaining solution for a (LDP) Linear Diophantine Problem (where $v$ > $n$) in $\mathbb N$ an NP-hard Problem too.

Now given the restricted ILP Problem with an additional constraint: