## You are here

HomeErd\H{o}s-Ginzburg-Ziv theorem

## Primary tabs

# Erdős-Ginzburg-Ziv theorem

If $a_{1},a_{2},\ldots,a_{{2n-1}}$ is a set of integers, then there exists a subset $a_{{i_{1}}},a_{{i_{2}}},\ldots,a_{{i_{n}}}$ of $n$ integers such that

$a_{{i_{1}}}+a_{{i_{2}}}+\cdots+a_{{i_{n}}}\equiv 0\;\;(\mathop{{\rm mod}}n).$ |

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. Zbl 0859.11003.
- 2 Hao,P. On a Congruence modulo a Prime Amer. Math. Monthly, vol. 113, (2006), 652-654

Keywords:

zero-sum

Synonym:

EGZ theorem

Type of Math Object:

Theorem

Major Section:

Reference

## Mathematics Subject Classification

20D60*no label found*11B50

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Jul 5

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

Jun 11

new question: binomial coefficients: is this a known relation? by pfb

Jun 6

new question: difference of a function and a finite sum by pfb

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

Jun 19

new question: Banach lattice valued Bochner integrals by math ias

Jun 13

new question: young tableau and young projectors by zmth

Jun 11

new question: binomial coefficients: is this a known relation? by pfb

Jun 6

new question: difference of a function and a finite sum by pfb