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 Theorem## Explore with Wolfram|Alpha

## Cite this as:

Weisstein, Eric W. "Genus Theorem." From
*MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/GenusTheorem.html