Fermat, Euler, and Pseudoprimes

  • David M. Bressoud
Part of the Undergraduate Texts in Mathematics book series (UTM)


We have reduced the problem of finding even perfect numbers to deciding when M(p) = 2 P — 1 is prime. Algorithm 2.9 is a very recent development. In this chapter we will be starting with some progress made by Pierre de Fermat (1601-1665) in 1640.


Prime Divisor Binary Representation Primality Test Small Divisor Distinct Integer 
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  1. R. D. Carmichael, “Note on a New Number Theory Function,” Bull. Am. Math. Soc., 16(1909-1910), 232–238.CrossRefGoogle Scholar
  2. R. D. Carmichael, “On composite numbers P which satisfy the Fermat congruence AP-1 ≡ 1 mod P,” Am. Math. Monthly, 19(1912), 22–27.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York, Inc. 1989

Authors and Affiliations

  • David M. Bressoud
    • 1
  1. 1.Mathematics and Computer Science DepartmentMacalester CollegeSaint PaulUSA

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