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Let A_1, ..., A_r be finite, nonempty sets of integers, and let h_1,..., h_r be positive integers. The linear formh_1A_1 + ··· + h_rA_r is the set of all integers of the form b_1 + ··· + b_r, where b_i is an integer that can be represented as the sum ofh_i elements of the set A_i. In this paper, the structure of the linear form h_1A_1 + ··· + h_rA_r is completely determined for all sufficiently large...
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