quadratic reciprocity
nounEtymology
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.
Definitions
The mathematical theorem which states that, for given odd prime numbers p and q, the…
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.
- Yes, but we need not only Quadratic Reciprocity but also Dirichlet's theorem on primes in arithmetic progressions to see this.
- Gauss studied these sorts of numbers while attempting to formulate and prove higher order reciprocity laws, following his success with quadratic reciprocity.
The neighborhood
Vish — recursive loop
No curated loop yet for quadratic reciprocity. Loops are being traced one word at a time while the ingestion pipeline matures.
sense glosses and etymology drawn from English Wiktionary · source · CC-BY-SA