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Hasse's Resolution Modulus Theorem

The Jacobi symbol (a/y)=chi(y) as a number theoretic character can be extended to the Kronecker symbol (f(a)/y)=chi^*(y) so that chi^*(y)=chi(y) whenever chi(y)!=0. When y is relatively prime to f(a), then chi^*(y)!=0, and for nonzero values chi^*(y_1)=chi^*(y_2) iff y_1=y_2 mod^+ f(a). In addition, |f(a)| is the minimum value for which the latter congruence property holds in any extension symbol for chi(y).

See also

Jacobi Symbol, Kronecker Symbol, Number Theoretic Character

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References

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

Referenced on Wolfram|Alpha

Hasse's Resolution Modulus Theorem

Cite this as:

Weisstein, Eric W. "Hasse's Resolution Modulus Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HassesResolutionModulusTheorem.html

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