| The New Upper Bounds of Some Ruzsa Numbers $R_m$ |
| Received:November 05, 2008 Revised:May 16, 2009 |
| Key Words:
Erd\H{o}s-Tur\'{a}n conjecture additive bases Ruzsa numbers.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.10901002; 10771103). |
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| Abstract: |
| For $A\subseteq {\mathbf{Z}}_m$ and $n\in {\mathbf{Z}}_m$, let $\sigma_A(n)$ be the number of solutions of equation $n=x y, x,y\in A$. Given a positive integer $m$, let $R_m$ be the least positive integer $r$ such that there exists a set $A\subseteq {\mathbf{Z}}_m$ with $A A={\mathbf{Z}}_m$ and $\sigma_A(n)\leq r$. Recently, Chen Yonggao proved that all $R_m\leq 288$. In this paper, we obtain new upper bounds of some special type $R_{kp^2}$. |
| Citation: |
| DOI:10.3770/j.issn:1000-341X.2010.03.021 |
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