Đề tài " Finite and infinite arithmetic progressions in sumsets "

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˝s and Folkman on complete sequences. o

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