# The Euclidean Algorithm and Applications

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## 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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