Finite Sums from Sequences Within Cells of a Partition of N

@article{Hindman1974FiniteSF,
title={Finite Sums from Sequences Within Cells of a Partition of N},
author={N. Hindman},
journal={J. Comb. Theory, Ser. A},
year={1974},
volume={17},
pages={1-11}
}

Abstract The principal result of this paper establishes the validity of a conjecture by Graham and Rothschild. This states that, if the natural numbers are divided into two classes, then there is a sequence drawn from one of those classes such that all finite sums of distinct members of that sequence remain in the same class.