Fermat's Polygonal Number Theorem states that every positive integer is a sum of at most n numbers of the n-gonal kind, meaning every positive integer can be written as the sum of three or fewer triangular numbers, four or fewer square numbers, five or fewer pentagonal numbers, and so on for every polygon size. In the language of additive number theory, the n-gonal numbers form an additive basis of order n.
Facts
StatementEvery positive integer is a sum of at most n n-gonal numbers. 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
Source Fermat polygonal number theorem (Wikipedia)
Named After
Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
Proved By
Sources
1. Fermat polygonal number theorem (Wikipedia)
Lead paragraph, sentence 1
Every positive integer is a sum of at most n n-gonal numbers.
History
finally proven by Cauchy in 1813
In Branch: Number Theory, Lead sentence
In additive number theory, the Fermat polygonal number theorem states that every positive integer is a sum of at most n n-gonal nu
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