, Volume 13, Issue 1-3, pp 333-337

On Kemnitz’ conjecture concerning lattice-points in the plane

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Abstract

In 1961, Erdős, Ginzburg and 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.

Dedicated to Richard Askey on the occasion of his 70th birthday.
2000 Mathematics Subject Classification Primary—11B50.