论文标题
在功能上$ sx $的添加剂补充
On function $SX$ of additive complements
论文作者
论文摘要
如果所有足够大的整数都可以表示为$ a $ a $ a和$ b $的两个元素的总和，则两个非负整数的$ a，b $称为\ emph {addive requements}。如果每个非负整数都可以唯一表示为$ a $ a $ a和$ b $的两个元素的总和，我们将进一步称为$ a，b $ \ emph {perfect添加剂}。令$ a（x）$为$ a $的计数函数。在本文中，我们关注函数$ sx $，其中$ sx = \ limsup_ {x \ rightArrow \ infty \ infty} \ frac {\ max \ {a（x），b（x）\}} {\ sqrt {x}} $由Erdős和Freeud crompots $ cromin crombote conderive a $ condive of a $ subrose a $。并进一步固定量。我们还为添加剂补充提供了$ SX $的绝对下限。
Two sets $A,B$ of nonnegative integers are called \emph{additive complements}, if all sufficiently large integers can be expressed as the sum of two elements from $A$ and $B$. We further call $A,B$ \emph{perfect additive complements} if every nonnegative integer can be uniquely expressed as the sum of two elements from $A$ and $B$. Let $A(x)$ be the counting function of $A$. In this paper, we focus on the function $SX$, where $SX=\limsup_{x\rightarrow\infty}\frac{\max\{A(x),B(x)\}}{\sqrt{x}}$ was introduced by Erdős and Freud in 1984. As a main result, we determine the value of $SX$ for perfect additive complements and further fix the infimum. We also give the absolute lower bound of $SX$ for additive complements.
