Lecture10StudentNotes

# Row i 1 2 3 4 5 6 7 8 x i y i r i qi 1 0 9870 0 1

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: hat 9870x + 2914y = gcd(9870, 2914). Row i 1 2 3 4 5 6 7 8 x i y i r i qi 1 0 9870 0 1 2914 GCD CT: If d &gt; 0, d|a, d|b and Take then from the second last row. Notice that and so Also, the second last row gives By GCD CT, Variations • If a or b is negative, apply the EEA to gcd(|a|, |b|) and then change the signs of x and y after the EEA is complete. • If a &lt; b, simply swap their places in the algorithm. This works because 4 Math 135: Lecture 10: Extended Euclidean Algorithm Exercise 10.12. In Exercise 9.8 you computed the gcd of two numbers. Repeat that exercise using the EEA. Use your results and GCD CT to verify your computed gcd. 5...
View Full Document

## This document was uploaded on 02/18/2014 for the course MATH 135 at Waterloo.

Ask a homework question - tutors are online