For distinct odd prime numbers p and q, the theorem relates the solvability of the congruence x squared is congruent to p modulo q to the solvability of x squared is congruent to q modulo p, via a precise sign rule. Gauss called it the 'golden theorem' of number theory and gave several of its many known proofs.
Facts
StatementThe law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. 1 Classification
Statement FormCharacterization Theorem 1 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. Quadratic Reciprocity (Wikipedia)
Wikimedia Foundationlead section, first paragraphQuote, lead section, first paragraph
In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.
2. Disquisitiones Arithmeticae (Wikipedia)
Wikimedia Foundationlead section, publication sentenceQuote, lead section, publication sentence
written in Latin by Carl Friedrich Gauss in 1798, when Gauss was 21, and published in 1801, when he was 24.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.