Abstract
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.
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Rosenthal, D., Rosenthal, D., Rosenthal, P. (2018). The Euclidean Algorithm and Applications. In: A Readable Introduction to Real Mathematics. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-00632-7_7
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DOI: https://doi.org/10.1007/978-3-030-00632-7_7
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-00631-0
Online ISBN: 978-3-030-00632-7
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