ABSTRACT
The subject matter of this chapter has strong algebraic content and is, in fact, largely a special case of basic group theory in abstract algebra. Of course, abstract algebra is not a prerequisite for this text, so the material will be developed from scratch in a number-theoretic setting. However, since it would be a pity not to understand this material in its proper context, occasional references to group theory will be made. These references can be ignored by people who are not interested in these algebraic connections. In proving the various facts quoted, the only properties of the real numbers that are used is the fact that they can be added, subtracted, multiplied and divided, and that the various standard rules of arithmetic hold. This chapter looks at a special kind of prime number that, on its face, seems to have nothing to do with perfect numbers, but which ultimately play an important role in their classification.
