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9870x + 2914y = gcd(9870, 2914). Row i
8 x i y i r i qi
1 0 9870
0 1 2914 GCD CT: If d > 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,
• 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 < 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...
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This document was uploaded on 02/18/2014 for the course MATH 135 at Waterloo.
- Spring '08