Hasse's Resolution Modulus Theorem

The Jacobi symbol  as a number theoretic 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 .

REFERENCES:

Cohn, H. Advanced Number Theory. New York: Dover, pp. 35-36, 1980.