The Jacobi Symbol as a Character can be extended to the Kronecker Symbol so that whenever . When is Relatively Prime to , then , and for Nonzero values Iff . In addition, is the minimum value for which the latter congruence property holds in any extension symbol for .
See also Character (Number Theory), Jacobi Symbol, Kronecker Symbol
Cohn, H. Advanced Number Theory. New York: Dover, pp. 35-36, 1980.