  We study central hyperplane arrangements with integral coefficients modulo
positive integers $q$. We prove that the cardinality of the complement of the
hyperplanes is a quasi-polynomial in two ways, first via the theory of
elementary divisors and then via the theory of the Ehrhart quasi-polynomials.
This result is useful for determining the characteristic polynomial of the
corresponding real arrangement. With the former approach, we also prove that
intersection lattices modulo $q$ are periodic except for a finite number of
$q$'s.
