Abstract
We describe the Euclidean Algorithm, 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. We also present a proof of Euler’s generalization of Fermat’s Theorem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Rosenthal, D., Rosenthal, D., Rosenthal, P. (2014). The Euclidean Algorithm and Applications. In: A Readable Introduction to Real Mathematics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-05654-8_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-05654-8_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05653-1
Online ISBN: 978-3-319-05654-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)