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Two infinite sequences A and B of nonnegative integers are called additive complements, if their sum contains all sufficiently large integers. We also say that B is an additive complement of A if A and B are additive complements. In this paper, we consider a problem of Ben Green on additive complements of the squares: S={12,22,…}. The following result is proved: if B={bn}n=1∞ with bn≥π216n2−0.57n12logn−βn12...
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