If p is a prime number and a is any integer not divisible by p, then a raised to the power p minus 1 is congruent to 1 modulo p. It underlies many primality tests and much of elementary number theory, and is a special case of Euler's theorem.
Facts
StatementFermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. 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.
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
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's Little Theorem (Wikipedia)
Wikimedia Foundationlead section, first paragraph
Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p.
History section, Euler proof sentence
Euler provided the first published proof in 1736
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