Solve ax+by=GCD(a,b) for RSA Algorithm Cryptography

[shivajikobardan]

Homework Statement

What's the technique used by this teacher to solve ax+by=GCD(a,b) in RSA Algorithm-Cryptography?

Relevant Equations

RSA Algorithm CT= (PT)^e mod n and PT=(CT)^d mod n

It starts at 6:16

It's the part where he's pointing his hand in this picture. I didn't get it although it's pretty mechanical, so I'd like to learn that technique as this is really useful in RSA algorithm(rather than having to memorize some values). I've been searching for a method like that since I saw this problem(been months) but could not find a technique like that. And it was always about just do it rather having any mechanical method like this one. So, I want to learn this.
Or, if you have any other simple methods to solve this equation, please tell me

 

[pasmith]

I believe this is Euclid's Algorithm. It is generally used to find GCD(a,b) but will obtain x and y in the process.

 

[shivajikobardan]

I believe this is Euclid's Algorithm. It is generally used to find GCD(a,b) but will obtain x and y in the process.

I'm trying to figure out a way to replicate his way. I found this
https://math.stackexchange.com/questions/691916/what-is-the-link-between-the-quotient-and-the-bézout-coefficients-in-the-extende

https://crypto.stackexchange.com/qu...lic-exponent-and-the-modulus-fact/54479#54479

But could not get it clearly with a table.

But I'm trying to find some examples around it. PS there are some cases of what happens when the number is greater or lesser than something, I want to know about it. Do share if you've any information regarding this thing.

Thanks for the information!