Lecture 2: The Euclidean Algorithm


This lecture discusses one of the earliest and most important mathematical algorithms. The Euclidean algorithm computes the greatest common divisor of two integers (it can be extended to other domains such as polynomials). This algorithm, not commonly taught when gcds are introduced in High School mathematics, is a much more efficient way to compute the gcd than using integer factorization.
The algorithm can be stated in a few lines, using recursion, yet it has many fascinating properties, and its complete analysis was a major undertaking.
An immediate generalization of the Euclidean algorithm, called the extended Euclidean algorithm computes integers x and y such that x*a + y*b = gcd(a,b). This relationship, called Bezout's identity, can be used to prove Theorem 1.1 from lecture 1. We will see later in the course, that it has many other important applications.

Background Material

Reading

Also study Maple's igcd, igcdex, gcd, and gcdex commands.

Topics

Maple worksheets and other resources

Assignments

This assignment is a practice assignment not intended to be handed in.
Created: Mar. 31, 2008 by jjohnson AT cs DOT drexel DOT edu