论文标题
关于添加剂补充的注释
A Note on Additive Complements
论文作者
论文摘要
如果它们的总和包含所有足够大的整数，则两个非阴性整数的无限序列A和B被称为附加互补。令$ a（x）$和$ b（x）$为A和B的计数函数。在本文中，我们在2016年扩展了刘和方的结果，并在添加剂补充上获得了一些结果。例如，我们证明存在添加剂补充$ a $ a和$ b $，以便$ \ limsup_ {x \ to+\ infty} a（x）b（x）b（x）/x = 2 $ and $ a（x）b（x）b（x）-x = 1 $ for Indluser -lutheral fortibal forsity for Intypotical Integers $ x $ x $。
Two infinite sequences A and B of non-negative integers are called additive complements, if their sum contains all sufficiently large integers. Let $A(x)$ and $B(x)$ be the counting functions of A and B. In this paper, we extend the results of Liu and Fang in 2016 and obtain some results on additive complements. For example, we prove that there exist additive complements $A$ and $B$ such that $\limsup_{x\to+\infty} A(x)B(x)/x= 2$ and $A(x)B(x) - x = 1$ for infinitely positive integers $x$.
