Set systems with no union of cardinality 0 modulo m

Let q be a prime power. It is shown that for any hypergraph ℱ = {F1,..., Fd(q-1)+1} whose maximal degree is d, there exists Ø ≠ ℱ0 ⊂ ℱ, such that[Figure not available: see fulltext.] ≡ 0 (mod q). © 1991 Springer-Verlag.