Schur's Theorem states that for any finite coloring of the positive integers, there exist three integers x, y and z of the same color satisfying x plus y equals z. Proved by Issai Schur, it is an early result in Ramsey theory that Schur originally developed while studying a version of Fermat's Last Theorem reduced modulo a prime.
Facts
StatementThe theorem states that for every positive integer c there is a positive integer S such that any partition of the integers from 1 to S into c parts puts some three integers x, y and z with x plus y equals z into the same part. 1 Classification
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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.
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.
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
Source Schur's Theorem (Ramsey Theory) (Wikipedia)
Sources
1. Schur's Theorem (Ramsey Theory) (Wikipedia)
Wikimedia FoundationWikipedia, Schur's theorem, Ramsey theory section
In Ramsey theory, Schur's theorem states that for every positive integer c, there exists a positive integer S, such that for every partition of the integers {1,…,S} into c parts, one of the parts contains integers x, y and z with x+y=z.
Proved By: Issai Schur, Lead paragraph
In discrete mathematics, Schur's theorem is any of several theorems of the mathematician Issai Schur. In differential geometry, Schur's theorem is a theorem
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