Linear programming over a finite field I have a system of equations $Ax = b$ over some finite field $\mathbb{Z}_p$ and want to find a feasible solution. I'm sure this problem is NP-hard, but I'm struggling to find any literature on the subject. Does this problem have a name? What is known about the computational complexity of this problem?
Your problem, solving a system of linear equations, can be solved using an ancient algorithm, Gaussian elimination, which works over all fields.

Note that linear programming is more general, allowing also inequalities. It is not entirely clear, however, how the order should be defined over a finite field.