Erdős sumset conjecture

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