  In this paper, we devise two algorithms for the problem of testing
$q$-monomials of degree $k$ in any multivariate polynomial represented by a
circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time
randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic
algorithm for the same $q$-monomial testing problem but requiring the
polynomials to be represented by tree-like circuits. Several applications of
$q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$
upper bound for the $m$-set $k$-packing problem.
