can be solved for a prime iff or . The representation is unique except for changes of sign or rearrangements of and . This theorem is intimately connected with the quadratic reciprocity theorem, and generalizes to the biquadratic reciprocity theorem.
Genus Theorem
See also
Composition Theorem, Diophantine Equation--4th Powers, Fermat's Theorem, Form Genus, Fundamental Theorem of Genera, Quadratic Reciprocity TheoremExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Genus Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GenusTheorem.html