Roots of Unity in ℤ/m

  • Lindsay N. Childs
Part of the Undergraduate Texts in Mathematics book series (UTM)


In this chapter we develop the information needed to prove Rabin’s theorem. We first count the number of nth 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.


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

Authors and Affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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