The Euclidean Algorithm and Applications

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


We describe the Euclidean Algorithm, which provides a way of expressing the greatest common divisor of two natural numbers as a “linear combination” of the numbers. This algorithm has a number of important applications, including forming the basis for a different proof of the Fundamental Theorem of Arithmetic. It is also an important ingredient in the RSA procedure for sending secret messages. A proof of Euler’s generalization of Fermat’s Little Theorem is also included.

Copyright information

© 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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