The mathematical theorem which states that, for given odd prime numbers p and q, the question of whether p is a squaremodulo q is equivalent to the question of whether q is a square modulo p.
Origin
The theorem highlights a particular form of reciprocity in the solvability of the quadratic equation a2 = b in modular arithmetic. It was conjectured by Leonhard Euler and Adrien-Marie Legendre and first proved by Carl Friedrich Gauss.
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