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Erdos -> Erdős + clean-up
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David Roberts
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EGZ theorem (ErdosErdős-Ginzburg-Ziv)

ErdosErdős, Ginzburg and Ziv prove the following: Let $n \geq 1$¸ and $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist distinct $i_1,\ldots , i_n$ such that: $$a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}$$$$ a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}. $$ Is there a proof that doesn't use Chevalley-Warningthe Chevalley–Warning theorem (or a variant of its proof)?

EGZ theorem (Erdos-Ginzburg-Ziv)

Erdos, Ginzburg and Ziv prove the following: Let $n \geq 1$¸ $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist distinct $i_1,\ldots , i_n$ such that: $$a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}$$ Is there a proof that doesn't use Chevalley-Warning theorem (or a variant of its proof)?

EGZ theorem (Erdős-Ginzburg-Ziv)

Erdős, Ginzburg and Ziv prove the following: Let $n \geq 1$ and $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist distinct $i_1,\ldots , i_n$ such that $$ a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}. $$ Is there a proof that doesn't use the Chevalley–Warning theorem (or a variant of its proof)?

added 9 characters in body
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darij grinberg
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Erdos, Ginzburg and Ziv prove the following: Let $n \geq 1$¸ $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist distinct $i_1,\ldots , i_n$ such that: $$a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}$$ Is there a proof that doesn't use Chevalley-Warning theorem (or a variant of its proof)?

Erdos, Ginzburg and Ziv prove the following: Let $n \geq 1$¸ $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist $i_1,\ldots , i_n$ such that: $$a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}$$ Is there a proof that doesn't use Chevalley-Warning theorem (or a variant of its proof)?

Erdos, Ginzburg and Ziv prove the following: Let $n \geq 1$¸ $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist distinct $i_1,\ldots , i_n$ such that: $$a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}$$ Is there a proof that doesn't use Chevalley-Warning theorem (or a variant of its proof)?

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Portland
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EGZ theorem (Erdos-Ginzburg-Ziv)

Erdos, Ginzburg and Ziv prove the following: Let $n \geq 1$¸ $a_1,\ldots, a_{2n-1}\in \mathbb{Z}$. There exist $i_1,\ldots , i_n$ such that: $$a_{i_1} + \cdots + a_{i_n} \equiv 0 \pmod{n}$$ Is there a proof that doesn't use Chevalley-Warning theorem (or a variant of its proof)?