论文标题
在具有总和和差异结构的集合上
On sets with sum and difference structure
论文作者
论文摘要
对于非空置的非负整数和整数$ n $，让$ r_ {a，b}（n）$是$ n $ as $ n $ as $ a+a+b $和$ d_ {a，b}（a，b}（n）$的表示$ n $ as $ n $ as $ a-a-b $的数量，$ n $ a a $ a-a-b $ a $ a a a b y a a b b be，在本文中，我们确定了$ a，b $的集合，使每个非负整数$ n $ $ r_ {a，b}（n）= 1 $。我们还考虑了\ emph {差异}结构并证明：存在设置$ a $ a $ a $ a和$ b $的非负整数，以至于所有大的$ n $，$ a（x）b（x）b（x）b（x）=（x）=（1+o（1+o（1+o（1+o（1+o（1+o（1+o）），$ r_ {a，b}（n）\ ge 1 $ an对于无限的许多积极整数$ n $。还包含其他相关结果。
For nonempty sets $A,B$ of nonnegative integers and an integer $n$, let $r_{A,B}(n)$ be the number of representations of $n$ as $a+b$ and $d_{A,B}(n)$ be the number of representations of $n$ as $a-b$, where $a\in A, b\in B$. In this paper, we determine the sets $A,B$ such that $r_{A,B}(n)=1$ for every nonnegative integer $n$. We also consider the \emph{difference} structure and prove that: there exist sets $A$ and $B$ of nonnegative integers such that $r_{A,B}(n)\ge 1$ for all large $n$, $A(x)B(x)=(1+o(1))x$ and for any given nonnegative integer $c$, we have $d_{A,B}(n)=c$ for infinitely many positive integers $n$. Other related results are also contained.
