Dual formulations for optimization problems provide a new way to view the same problem, revealing its structure and bounding optimal solutions. A strong dual formulation constructs a problem that can be solved in place of or alongside the primal and converges on the same solution. In this paper we examine the general dual framework for nonlinear programs suggested by Everett and developed by Gould. This is leveraged to provide the first known strong dual formulation with a finite-dimensional domain for general integer linear programming. In particular, the dual problem optimizes three variables subject to a bounded, exponential number of constraints. The zero duality gap as well as small domain may prove useful in developing new techniques for solving integer linear programs.