A Concrete Introduction to Higher Algebra pp 378-396 | Cite as

# Roots of Unity in ℤ/*m*ℤ

Chapter

## Abstract

In this chapter we develop the information needed to prove Rabin’s theorem. We first count the number of *n*th roots of 1 or of −1 modulo *m* for any *n* and *m*. This allows us to count, for any odd composite number *m*, the number of false witnesses for *m*—that is, the number of numbers a modulo *m* such that *m* is a strong *a*-pseudoprime. These techniques yield a proof of Rabin’s theorem. We conclude the chapter with some observations about designing RSA codes related to strong *a*-pseudoprime testing.

## Keywords

Prime Divisor Primitive Element Great Common Divisor Primitive Root Chinese Remainder Theorem
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## Copyright information

© Springer Science+Business Media New York 1995