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 Erdos. 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.
- Almost periodic functions
- Sum sets
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty