Consider proper equivalence classes of forms with discriminant equal to the field discriminant, then they can be subdivided equally into genera of forms which form a subgroup of the proper equivalence class group under composition (Cohn 1980, p. 224), where is the number of distinct prime divisors of . This theorem was proved by Gauß in 1801.

**References**

Arno, S.; Robinson, M. L.; and Wheeler, F. S. ``Imaginary Quadratic Fields with Small Odd Class Number.'' http://www.math.uiuc.edu/Algebraic-Number-Theory/0009/.

Cohn, H. *Advanced Number Theory.* New York: Dover, 1980.

Gauss, C. F. *Disquisitiones Arithmeticae.* New Haven, CT: Yale University Press, 1966.

© 1996-9

1999-05-26