Euler’s Function

  • Gareth A. Jones
  • J. Mary Jones
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


One of the most important functions in number theory is Euler’s function φ(n), which gives the number of congruence classes [a] ∈ ℤn which have an inverse under multiplication. We shall see how to evaluate this function, study its basic properties, and see how it can be applied to various problems such as the calculation of large powers and the encoding of secret messages.


Secret Message Decimal Digit Congruence Class Multiplicative Inverse Frequent Letter 
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Copyright information

© Springer-Verlag London 1998

Authors and Affiliations

  • Gareth A. Jones
    • 1
  • J. Mary Jones
    • 2
  1. 1.School of MathematicsUniversity of SouthamptonHighfieldUK
  2. 2.The Open UniversityWalton HallUK

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