Let p be a large prime number, and U, V be nonempty subsets of the set of residue classes modulo p. In this paper we obtain results on the distribution and the additive properties of sequences involving terms of the form u + v, where u ∈ U and v ∈ V. For instance, we prove that (A+A)(B +Y)+(C +C)(D +W) = Fp, for any subsets A, B, C, D,Y, W of F? p with |A||C|, !|B||D||Y||W| ≥ 10 p. This extends a previous result of Garaev and the author.
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机译：让P是一个大的素数，而U，V是该组残留类模数的非空的子集。在本文中，我们获得了涉及形式U + V的序列的分布和添加剂性能的结果，其中U≠U和V≠V.例如，我们证明了（A + A）（B + Y）+ （C + C）（D + W）= FP，对于任何子集A，B，C，D，Y，W的F？ p用| a || c |，！| b || d || y || w | ≥10p。这扩展了Garaev和作者的先前结果。
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