  In 1961, P. Erd\H{o}s, A. Ginzburg, and A. Ziv proved a remarkable theorem
stating that each set of $2n-1$ integers contains a subset of size $n$, the sum
of whose elements is divisible by $n$. We will prove a similar result for pairs
of integers, i.e., planar lattice points, usually referred to as Kemnitz'
conjecture.
