Question

How did the 7 x 13 - 30 x 3 happen and where did the 13...

How did the 7 x 13 - 30 x 3 happen and where did the 13 come from. Please explain with details.

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https://www.chegg.com/homework-help/questions-and-answers/7-x-13-30-x-3-happen-13-come--please-explain-details-q39329141?trackid=U3ocWz5H

Math   Advanced-Math   
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Homework Answers

Answer #1

The first step is from the third step of Euclidean algorithm

Next, we use the second step of Euclidean algorithm to get and substitute this expression for in

To get

Expanding this we get

Which is

Collecting terms, we get

which is the expression

This is a very important and useful technique to calculated a linear combination equal to the GCD of a pair of integers

Hope this was helpful. Please do leave a positive rating if you liked this answer. Thanks and have a good day!

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