Olson's theorem
From Egres Open
Theorem (Olson [1]). Let q be a prime power, and let A be an [math]m \times n[/math] integer matrix, where [math]m \geq (q-1)n+1[/math]. There exists a non-empty subset of the columns of A such that every coordinate of the sum of these columns is divisible by q.
This is actually a special case of a theorem of Olson on finite Abelian groups that appeared in [1].
