quadratic reciprocity
Word Rarity
Rare
Frequency: Zipf frequency 2.71 in modern English
41
Scrabble Score
20
Letters
5
Syllables
12
Unique Chars
Meaning
noun
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
Example Sentences
- "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."
- "An interesting consequence of the above algorithm is that one can evaluate the Jacobi symbol in deterministic polynomial time in certain cases analogous to the way (“reduce and flip”) that one computes this symbol using quadratic reciprocity in the case F#61;#92;mathbb#123;Q#125;."
Etymology
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.
Usage
Inflected Forms
law of quadratic reciprocity (alternative)