legendre symbol
Word Rarity
Very rare
Frequency: Zipf frequency 2.23 in modern English
23
Scrabble Score
14
Letters
4
Syllables
11
Unique Chars
Meaning
noun
A mathematical function of an integer and a prime number, written (a/p), which indicates whether a is a quadratic residue modulo p.
Example Sentences
- "1994, James K. Strayer, Elementary Number Theory, Waveland Press, 2002, Reissue, page 109, Our only method at present for the computation of Legendre symbols requires a possible consideration of (p-1)/2 congruences (unless, of course, we are fortunate enough to encounter the desired quadratic residue along the way)."
- "The Jacobi symbol, which generalizes the Legendre symbol, sheds some additional light on how to determine whether (7.29) has solutions when m has two or more distinct prime factors."
- "Jacobi symbols can be used to facilitate the calculation of Legendre symbols. In fact, Legendre symbols can be eventually calculated by Jacobi symbols [17]. That is, the Legendre symbol can be calculated as if it were a Jacobi symbol. For example, consider the Legendre symbol #92;left(#92;frac#123;335#125;#123;2999#125;#92;right) where 335 = 5·67 is not a prime (of course, 2999 is a prime, otherwise, it is not a Legendre symbol)."
Etymology
Named after French mathematician Adrien-Marie Legendre (1752–1833), who introduced the symbol in 1798 in his work Essai sur la Théorie des Nombres ("Essay on the Theory of Numbers").