A positive answer to the Owings's sumsets question

Wen Huang; Zhengxing Lian; Song Shao; Rongzhong Xiao; Leiye Xu; Shuhao Zhang

A positive answer to the Owings's sumsets question

Combinatorics 2026-07-19 v1 Dynamical Systems Number Theory

Authors: Wen Huang , Zhengxing Lian , Song Shao , Rongzhong Xiao , Leiye Xu , Shuhao Zhang

Abstract

The paper gives a positive answer to Owings's sumsets question. That is, it is shown that for any $2$ -coloring of natural numbers, there is an infinite $B\subset \mathbb{N}$ such that $B+B$ is monochromatic. Meanwhile, some weighted forms of this result are also presented.

Keywords

Owings's sumsets monochromatic 2-coloring natural numbers infinite subsets weighted forms

Cite

@article{arxiv.2607.17333,
  title  = {A positive answer to the Owings's sumsets question},
  author = {Wen Huang and Zhengxing Lian and Song Shao and Rongzhong Xiao and Leiye Xu and Shuhao Zhang},
  journal= {arXiv preprint arXiv:2607.17333},
  year   = {2026}
}

Comments

20 pages. Comments are welcome