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