This question was probably asked before but here goes. I have a convex polytope given by $Ax\leq b$ for a specific integer matrix $A$ and integer vector $b$. I need a simple method/result on how to check existence of a lattice point inside this polytope. I realize that this is not a very precise request but any kind of input would be nice. I'm not sure if it matters but $A$ is a sparse matrix.