Fermat’s Little Theorem and Wilson’s Theorem

  • Daniel Rosenthal
  • David Rosenthal
  • Peter Rosenthal
Part of the Undergraduate Texts in Mathematics book series (UTM)


Fermat’s Little Theorem states that, for every prime number p, if p does not divide the natural number a, then a to the power p − 1 leaves a remainder of 1 upon division by p. This beautiful theorem has a number of important theoretical and practical applications, one of which is to the technique for sending secret messages that is described in Chapter  6. We present proofs of Fermat’s Little Theorem and also of Wilson’s Theorem, another beautiful formula in modular arithmetic.

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Daniel Rosenthal
    • 1
  • David Rosenthal
    • 2
  • Peter Rosenthal
    • 3
  1. 1.TorontoCanada
  2. 2.Department of Mathematics and Computer ScienceSt. John’s UniversityQueensUSA
  3. 3.Department of MathematicsUniversity of TorontoTorontoCanada

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