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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. Due to its subtlety, it has many formulations, but the most standard statement is: Law of quadratic reciprocity — Let p and q be distinct odd prime numbers, and define the Legendre symbol as: Then: indeed, This formula only works if it is known in advance that is a quadratic residue, which can be checked using the law of quadratic reciprocity.

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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. Due to its subtlety, it has many formulations, but the most standard statement is: Law of quadratic reciprocity — Let p and q be distinct odd prime numbers, and define the Legendre symbol as: Then: indeed, This formula only works if it is known in advance that is a quadratic residue, which can be checked using the law of quadratic reciprocity. (en)
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