A reciprocity theorem for the case 
solved by Gauss using "integers"
of the form 
, when 
is a root of 
(i.e., 
equals 
or 
) and 
, 
are integers.
Cubic Reciprocity Theorem
See also
Cubic Residue, Reciprocity TheoremExplore with Wolfram|Alpha
References
Ireland, K. and Rosen, M. "Cubic and Biquadratic Reciprocity." Ch. 9 in A Classical Introduction to Modern Number Theory, 2nd ed. New York: Springer-Verlag, pp. 108-137, 1990.Referenced on Wolfram|Alpha
Cubic Reciprocity TheoremCite this as:
Weisstein, Eric W. "Cubic Reciprocity Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CubicReciprocityTheorem.html