Given any 2n minus 1 integers, some n of them sum to a multiple of n. A foundational result in zero-sum Ramsey theory, it was proved by Paul Erdos, Abraham Ginzburg and Abraham Ziv.
Facts
StatementAny multiset of 2n minus 1 integers from the integers modulo n contains a subset of exactly n elements whose sum is a multiple of n, and 2n minus 1 is the smallest size for which this always holds; a multiset of only 2n minus 2 integers need not contain such a subset. 1 Classification
Statement Form Connections
Sources
1. Erdos-Ginzburg-Ziv Theorem (Wikipedia)
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The classic result in this area is the 1961 theorem of Paul Erdős, Abraham Ginzburg, and Abraham Ziv.
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