| Version current |
Version 3 |
| If $a_1, a_2,\dotsc, a_{2n-1}$ is a set of integers, then there exists a subset $a_{i_1}, a_{i_2},\dotsc,a_{i_n}$ of $n$ integers such that |
If $a_1, a_2,\dotsc, a_{2n-1}$ is a set of integers, then there exists a subset $a_{i_1}, a_{i_2},\dotsc,a_{i_n}$ of $n$ integers such that |
| \begin{equation*} |
\begin{equation*} |
| a_{i_1}+ a_{i_2}+\dotsb+a_{i_n}\equiv 0 \pmod n. |
a_{i_1}+ a_{i_2}+\dotsb+a_{i_n}\equiv 0 \pmod n. |
| \end{equation*} |
\end{equation*} |
| The theorem is also known as the EGZ theorem. |
|
|
|
| \begin{thebibliography}{1} |
\begin{thebibliography}{1} |
|
|
| \bibitem{cite:nathanson_classicalbases} |
\bibitem{cite:nathanson_classicalbases} |
| Melvyn~B. Nathanson. |
Melvyn~B. Nathanson. |
| \newblock {\em Additive Number Theory: Inverse Problems and Geometry of |
\newblock {\em Additive Number Theory: Inverse Problems and Geometry of |
| Sumsets}, volume 165 of {\em GTM}. |
Sumsets}, volume 165 of {\em GTM}. |
| \newblock Springer, 1996. |
\newblock Springer, 1996. |
| \newblock \PMlinkexternal{Zbl 0859.11003}{http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003}. |
\newblock \PMlinkexternal{Zbl 0859.11003}{http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003}. |
| \bibitem{cite:haopan} |
|
| \newblock Hao,P. {\em On a Congruence modulo a Prime} |
|
| \newblock Amer. Math. Monthly, vol. 113, (2006), 652-654 |
|
|
|
| \end{thebibliography} |
\end{thebibliography} |
|
|
| %@BOOK{cite:nathanson_inverseprob, |
%@BOOK{cite:nathanson_inverseprob, |
| % author = {Melvyn B. Nathanson}, |
% author = {Melvyn B. Nathanson}, |
| % title = {Additive Number Theory: Inverse Problems and Geometry of Sumsets}, |
% title = {Additive Number Theory: Inverse Problems and Geometry of Sumsets}, |
| % series = {GTM}, |
% series = {GTM}, |
| % volume = 165, |
% volume = 165, |
| % year = 1996, |
% year = 1996, |
| % publisher = {Springer} |
% publisher = {Springer} |
| %} |
%} |
| % |
% |
