Euler's Criterion is a formula for determining whether an integer is a quadratic residue modulo an odd prime: for a prime p and an integer a coprime to p, a raised to the power of half of p minus one is congruent to one modulo p exactly when some integer squared is congruent to a modulo p, and congruent to negative one modulo p otherwise. The criterion can be restated concisely using the Legendre symbol, and it dates from a 1748 paper by Leonhard Euler.
Facts
StatementA formula for determining whether an integer is a quadratic residue modulo a prime. 1 Classification
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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.
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Source Euler's criterion (Wikipedia)
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Derived from the theorem's own name (unambiguous possessive-token match to exactly one live mathematician entity, w-bfill-g5-0924 browse backfill)
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Sources
1. Euler's criterion (Wikipedia)
Intro, sentence 1
Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime
Intro, sentence after the Legendre symbol reformulation
The criterion dates from a 1748 paper by Leonhard Euler.
In Branch: Number Theory, Lead sentence
In number theory, Euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime.
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