A Prime can be represented in an essentially unique manner in the form for integral and
Iff
or . It can be restated by letting

then all Relatively Prime solutions to the problem of representing for any Integer are achieved by means of successive applications of the Genus Theorem and Composition Theorem. There is an analog of this theorem for Eisenstein Integers.

**References**

Shanks, D. *Solved and Unsolved Problems in Number Theory, 4th ed.* New York: Chelsea, pp. 142-143, 1993.

© 1996-9

1999-05-26