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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: Prime numbers out of sequence by Rubens373

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new question: how to contest an entry? by zorba

new question: simple question by parag

new question: Prime numbers out of sequence by Rubens373

Oct 7

new question: Lorenz system by David Bankom

Oct 19

new correction: examples and OEIS sequences by fizzie

Oct 13

new correction: Define Galois correspondence by porton

Oct 7

new correction: Closure properties on languages: DCFL not closed under reversal by babou

new correction: DCFLs are not closed under reversal by petey

Oct 2

new correction: Many corrections by Smarandache

Sep 28

new question: how to contest an entry? by zorba

new question: simple question by parag