Resumen de Finite and infinite arithmetic progressions in sumsets

V.H. Vu, B. Szemerédi

• We prove that if A is a subset of at least cn1/2 elements of {1, . . . , n}, where c is a sufficiently large constant, then the collection of subset sums of A contains an arithmetic progression of length n. As an application, we confirm a long standing conjecture of Erd¿os and Folkman on complete sequences.