In additive number theory, Kemnitz's conjecture states that every set of 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
[3] In 2000, Lajos Rónyai proved a weakened form of Kemnitz's conjecture for sets with
[4] Then, in 2003, Christian Reiher proved the full conjecture using the Chevalley–Warning theorem.