A proof of a sumset conjecture of Erdős

Donald Robertson, Joel Moreira, Florian Richter

Research output: Contribution to journalArticlepeer-review


In this paper we show that every set A ⊂ ℕ with positive density contains B + C for some pair B, C of infinite subsets of ℕ , settling a conjecture of Erdős. The proof features two different decompositions of an arbitrary bounded sequence into a structured component and a pseudo-random component. Our methods are quite general, allowing us to prove a version of this conjecture for countable amenable groups.
Original languageEnglish
Pages (from-to)605-652
JournalAnnals of Mathematics
Issue number2
Publication statusPublished - 1 Mar 2019


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