Erdős sumset conjecture

In additive combinatorics, the Erdős sumset conjecture is a conjecture which states that if a subset ${\displaystyle A}$ of the natural numbers ${\displaystyle \mathbb {N} }$ has a positive upper density then there are two infinite subsets ${\displaystyle B}$ and ${\displaystyle C}$ of ${\displaystyle \mathbb {N} }$ such that ${\displaystyle A}$ contains the sumset ${\displaystyle B+C}$.[1][2] It was posed by Paul Erdős, and was proven in 2019 in a paper by Joel Moreira, Florian Richter and Donald Robertson.[3]