In this paper we show that every set AN 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.
MSC Codes 05D10, 11P70, 37A99, 46C99
|Original language||English (US)|
|State||Published - Mar 1 2018|
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