中文摘要：

设A和B是正整数集合，若它们的和A＋B={a＋b：a∈A，b∈B）包含所有充分大的整数，则称A，B为加法补集．本文推广了陈永高和方金辉关于加法补集的一个结论，特别证明了：存在加法补集A，B满足limsupx→∞[A（x）B（x）]/z=22/13，而且存在无穷多个正整数x使得A（x）B（x）-x=1。

英文摘要：

We call two sets A and B of non-negative integers additive complements if their sum contains all sufficiently large integers. Let A（x） and B（x） be the counting functions of A and B, respectively. In this paper, we extend the result in [Proc. Amer. Math. Soc., 2011, 139（3）： 881-883]. In particular, we prove that there exist additive complements A and B such that limsupx→∞[A（x）B（x）]/z=22/13 and A（x）B（x） - x = 1 for infinitely many positive integers x.