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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 ${\displaystyle B+C}$. 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

Notes

1. Di Nasso, Mauro; Goldbring, Isaac; Jin, Renling; Leth, Steven; Lupini, Martino; Mahlburg, Karl (2015), "On a sumset conjecture of Erdős" (PDF), Canadian Journal of Mathematics, 67 (4): 795–809, arXiv:1307.0767, doi:10.4153/CJM-2014-016-0, S2CID 15626732
2. "Erdős Sumset conjecture". 20 August 2017.
3. Moreira, Joel; Richter, Florian (March 2019). "A proof of a sumset conjecture". Annals of Mathematics. 189 (2): 605–652. arXiv:1803.00498. doi:10.4007/annals.2019.189.2.4. JSTOR 10.4007/annals.2019.189.2.4. S2CID 119158401. Retrieved 16 July 2020.

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