PlanetMath: Erdős-Ginzburg-Ziv theorem

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Erdős-Ginzburg-Ziv theorem

(Theorem)

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 integers such that

$\displaystyle a_{i_1}+ a_{i_2}+\dotsb+a_{i_n}\equiv 0 \pmod n.$

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

"Erdős-Ginzburg-Ziv theorem" is owned by bbukh. [ full author list (2) ]

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Other names:

EGZ theorem

Keywords:

zero-sum

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Cross-references: subset, integers

This is version 4 of Erdős-Ginzburg-Ziv theorem, born on 2003-06-07, modified 2006-08-07.
Object id is 4327, canonical name is ErdHosGinzburgZivTheorem.
Accessed 3393 times total.

Classification:

AMS MSC:	11B50 (Number theory :: Sequences and sets :: Sequences )
	20D60 (Group theory and generalizations :: Abstract finite groups :: Arithmetic and combinatorial problems)

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