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Pseudoprimes

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

Abstract

This chapter returns to the question of deciding whether a given odd number m is prime. The a-pseudoprime test of Chapter 10D will not work on Carmichael numbers. We first describe a recent idea of Alford which shows that there are many Carmichael numbers. Then we develop the strong a-pseudoprime test and present a theorem of Rabin that every composite number m fails the strong a-pseudoprime test for most a < m. We conclude this chapter with a proof of a weak version of Rabin’s theorem; the next chapter gives a proof of the strong version of Rabin’s theorem.

Keywords

Chinese Remainder Theorem Congruence Class Composite Number Generalize Riemann Hypothesis Primitive Root Modulo 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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