Erd\H{o}s-Ginzburg-Ziv theorem
ErdHosGinzburgZivTheorem
2003-06-07 19:31:50
2006-08-07 17:53:25
Theorem
zero-sum
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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*}
a_{i_1}+ a_{i_2}+\dotsb+a_{i_n}\equiv 0 \pmod n.
\end{equation*}
The theorem is also known as the EGZ theorem.
\begin{thebibliography}{1}
\bibitem{cite:nathanson_classicalbases}
Melvyn~B. Nathanson.
\newblock {\em Additive Number Theory: Inverse Problems and Geometry of
Sumsets}, volume 165 of {\em GTM}.
\newblock Springer, 1996.
\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}
%@BOOK{cite:nathanson_inverseprob,
% author = {Melvyn B. Nathanson},
% title = {Additive Number Theory: Inverse Problems and Geometry of Sumsets},
% series = {GTM},
% volume = 165,
% year = 1996,
% publisher = {Springer}
%}
%