In additive number theory, Kemnitz's conjecture states that every set of integer lattice points in the plane has a large subset whose centroid is also a lattice point. It was proved independently in the autumn of 2003 by Christian Reiher, then an undergraduate student, and Carlos di Fiore, then a high school student. [1]
The exact formulation of this conjecture is as follows:
Kemnitz's conjecture was formulated in 1983 by Arnfried Kemnitz [2] as a generalization of the Erdős–Ginzburg–Ziv theorem, an analogous one-dimensional result stating that every integers have a subset of size whose average is an integer. [3] In 2000, Lajos Rónyai proved a weakened form of Kemnitz's conjecture for sets with lattice points. [4] Then, in 2003, Christian Reiher proved the full conjecture using the Chevalley–Warning theorem. [5]