科研之友
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摘要
Text. 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 = {1(2), 2(2), ... }. The following result is proved: if B = {b(n)}(n=1)(infinity) with b(n) >= pi(2)/16 n(2) - 0.57n(1/2) log n - beta n(1/2). for all positive integers n and any given constant beta, then B is not an additive complement of S. In particular, B = {left perpendicular pi(2)/16 n(2) right perpendicular vertical bar n = 1, 2, ... } is not an additive complement of S. Video. For a video summary of this paper, please visit https://youtu.be/cVXWCP4Igp8.
