| Unique Weighted Representation Basis of Integers |
| Received:April 03, 2013 Revised:June 04, 2013 |
| Key Words:
additive basis representation function.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.10901002) and the Natural Science Foundation of Anhui Province (Grant No.1208085QA02). |
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| Abstract: |
| 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 $n=k_{1}a_{1}+k_{2}a_{2},$ $a_{1}, a_{2}\in A$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.03.010 |
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