---
tag: D5WSHR29WE
kind: statement
role: proposition
name: Erdős sumset conjecture
sources:
  - wikipedia: en:64308146@r1212046137
    locator: Erdős sumset conjecture
    note: adopted
    mention: wikipedia://en/64308146
    sections: [Statement]
same_as:
  wikidata: Q104844985
  wikipedia: Erdős sumset conjecture
inventory: [QV39RHNEBP]
---

## Statement

In additive combinatorics, the **Erdős sumset conjecture** is a conjecture which states that if a subset $A$ of the [[natural numbers|0MWKJ44V5A]] $\mathbb{N}$ has a positive upper density then there are two infinite subsets $B$ and $C$ of $\mathbb{N}$ such that $A$ contains the sumset $B+C$. It was posed by Paul Erdős, and was proven in 2019 in a paper by Joel Moreira, Florian Richter and Donald Robertson.