Erdős-Ginzburg-Ziv theorem
If ${a}_{1},{a}_{2},\mathrm{\dots},{a}_{2n-1}$ is a set of integers, then there exists a subset ${a}_{{i}_{1}},{a}_{{i}_{2}},\mathrm{\dots},{a}_{{i}_{n}}$ of $n$ integers such that
$${a}_{{i}_{1}}+{a}_{{i}_{2}}+\mathrm{\cdots}+{a}_{{i}_{n}}\equiv 0\phantom{\rule{veryverythickmathspace}{0ex}}(modn).$$ |
The theorem is also known as the EGZ theorem.
References
- 1 Melvyn B. Nathanson. Additive Number Theory: Inverse Problems and Geometry of Sumsets, volume 165 of GTM. Springer, 1996. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0859.11003Zbl 0859.11003.
- 2 Hao,P. On a Congruence^{} modulo a Prime Amer. Math. Monthly, vol. 113, (2006), 652-654
Title | Erdős-Ginzburg-Ziv theorem |
---|---|
Canonical name | ErdHosGinzburgZivTheorem |
Date of creation | 2013-03-22 13:40:00 |
Last modified on | 2013-03-22 13:40:00 |
Owner | bbukh (348) |
Last modified by | bbukh (348) |
Numerical id | 7 |
Author | bbukh (348) |
Entry type | Theorem |
Classification | msc 20D60 |
Classification | msc 11B50 |
Synonym | EGZ theorem |