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:
“Whatever we inherit from the fortunate
We have taken from the defeated
What they had to leave us—a symbol:
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—T.S. (Thomas Stearns)