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
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Proved By
Sources
1. Erdos-Ginzburg-Ziv Theorem (Wikipedia)
Wikimedia FoundationLead sectionQuote, Lead section
The classic result in this area is the 1961 theorem of Paul Erdős, Abraham Ginzburg, and Abraham Ziv.
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