In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo a prime number p: its value on a (nonzero) quadratic residue mod p is 1 and on a quadratic non-residue is −1.
The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity. Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order. The notational convenience of the Legendre symbol inspired introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol.
Read more about Legendre Symbol: Definition, Properties of The Legendre Symbol, Legendre Symbol and Quadratic Reciprocity, Related Functions, Computational Example
Famous quotes containing the word symbol:
“Every natural fact is a symbol of some spiritual fact. Every appearance in nature corresponds to some state of the mind, and that state of the mind can only be described by presenting that natural appearance as its picture.”
—Ralph Waldo Emerson (1803–1882)