quadratic reciprocity

名词 n.
中文释义

英文释义

名词 n.
  1. The mathematical theorem which states that, for given odd prime numbers p and q, the question of whether p is a square modulo q is equivalent to the question of whether q is a square modulo p. uncountable
    — Yes, but we need not only Quadratic Reciprocity but also Dirichlet's theorem on primes in arithmetic progressions to see this.

词形变化

law of quadratic reciprocity alternative

词源

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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