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# 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*

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new question: Prove a formula is part of the Gentzen System by LadyAnne

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new question: A problem about Euler's totient function by mbhatia

new problem: Problem: Show that phi(a^n-1), (where phi is the Euler totient function), is divisible by n for any natural number n and any natural number a >1. by mbhatia

new problem: MSC browser just displays "No articles found. Up to ." by jaimeglz

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new correction: underline-typo by Filipe

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new image: plot W(t) = P(waiting time <= t) (2nd attempt) by robert_dodier

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new image: plot W(t) = P(waiting time <= t) by robert_dodier