Course notes (chap. 1 Number Theory, chap. 2 ... - McGill University

1.4.1 Legendre and Jacobi Symbols
For an odd prime number p,wedefinetheLegendresymbol(Maplelegendre)
as
⎧
( a
⎨ +1 if a ∈ QR p
= −1 if a ∈ QNR p
p)
⎩
0 if p|a
For any integer n = p 1 p 2 ...p k ,wedefinetheJacobisymbol(Maplejacobi)
(a generalization of the Legendre symbol) as
( ( )( ) ( )
a a a a
=
...
n)
p 1 p 2 p k
Adrien-Marie Legendre
Carl Gustav Jacob Jacobi