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    Quadratic Reciprocity Theorem

    Basic definition

    The quadratic reciprocity theorem is a theorem that tells whether a quadratic equation modulo a prime has a solution.

    Detailed definition

    If p and q are distinct odd primes, then the quadratic reciprocity theorem states that the congruences
 x^2 congruent q (mod p) 
 x^2 congruent p (mod q) 
are both solvable or both unsolvable unless both p and q leave the remainder 3 when divided by 4 (in which case one of the congruences is solvable and the other is not).

    Educational grade level

    college level

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