The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other...

Carl Gustav Jacob Jacobi (/dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions...

symbol, written as ( a n ) {\displaystyle \left({\frac {a}{n}}\right)} or ( a | n ) {\displaystyle (a|n)} , is a generalization of the Jacobi symbol to...

Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order. The notational convenience of the Legendre symbol inspired introduction...

doubly-periodic functions Jacobi polynomials, a class of orthogonal polynomials Jacobi symbol, a generalization of the Legendre symbol Jacobi coordinates, a simplification...

it is 0 if p divides a. The same notation is used for the Jacobi symbol and Kronecker symbol, which are generalizations where p is respectively any odd...

function and a certain Dirichlet L-function The Jacobi symbol is a generalization of the Legendre symbol; the main difference is that the bottom number...

and let ( D n ) {\displaystyle \left({\tfrac {D}{n}}\right)} be the Jacobi symbol. We define δ ( n ) = n − ( D n ) . {\displaystyle \delta (n)=n-\left({\tfrac...

and p. This interpretation of the Legendre symbol as the sign of a permutation can be extended to the Jacobi symbol ( a n ) , {\displaystyle \left({\frac {a}{n}}\right)...

{a}{n}}\right)} is the Jacobi symbol. If n is an odd composite integer that satisfies the above congruence, then n is called an Euler–Jacobi pseudoprime (or...