整数集的唯一加权表示基

Unique Weighted Representation Basis of Integers

中文关键词:  加法基  表示函数.

英文关键词:additive basis  representation function.

中文摘要:

      令$k_{1}, k_{2}$为满足$(k_1,k_2)=1$且$k_{1}k_{2}\neq-1$的非零整数. 在本文中, 我们证明了存在集合$A\subseteq\mathbb{Z}$使得每个整数$n$都可以唯一地表示成$n=k_{1}a_{1}+k_{2}a_{2},$ 其中$a_{1},$ $a_{2}\in A.$

英文摘要:

      Let $k_{1}, k_{2}$ be nonzero integers with $(k_{1},k_{2})=1$ and $k_{1}k_{2}\neq-1$. In this paper, we prove that there is a set $A\subseteq\mathbb{Z}$ such that every integer can be represented uniquely in the form $n=k_{1}a_{1}+k_{2}a_{2},$ $a_{1}, a_{2}\in A$.