Structure Theorem for Multiple Addition and the Frobenius Problem Original Research Article

LetAsubset of or equal to[0; l] be a set ofnintegers, and lethgreater-or-equal, slanted2. By how much does hA exceed (h−1) A ? How can one estimate hA in terms ofn, l? We give sharp lower bounds extending and generalizing the well-known theorem of Freiman for 2A. A number of applications are provided as well. In particular, we give a solution for the old extremal problem of Frobenius–Erdimages–Graham concerning estimating of the largest integer, non-representable by a linear form. In a sense, our solution can not be improved.