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 Connections
Sources
1. Quadratic Reciprocity (Wikipedia)
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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)
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written in Latin by Carl Friedrich Gauss in 1798, when Gauss was 21, and published in 1801, when he was 24.
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