Super clear - the point about treating the underlined numbers as variables was key.

Dude taught in 15 minutes what my boolean algebra teacher couldn't in a week.

Euclid and Bezout were on drugs that day

Best and simplest explanation on KZfaq . Thanks

Treating the underlined numbers as variables was a game changer...Thank you so much @John Bowers

Showing the underlining of the numbers really was the missing link for my brain to understand this! Thank you!

This guy is the best explanator of such a complicated thing. Everything in simple words and step by step. THANKS

This is the best video I've seen on the extended Euclidean. The pointer at 9:50- to treat the number as if they were variables- is a critical step for people learning this for the first time. A lot of other videos speed through this critical step.

Thank you for this video! Been trying to get this right for quite some time and have watched several other lessons. When you said to treat the numbers as variables was really when it became clear to me! Well done! You really saved me from failing my exam!

GREAT explanation. As others have noted, treating the numbers as variables is what ultimately unlocked this for me. It's so unlike anything I've done previously in my limited math experience, I could not tell what was happening until this video made it clear. Thanks a lot!

The perfect math video doesn’t exi-

Wonderful explanation. I watched several videos, and this was the only one that really made me understand the substitution process. Thanks!

I missed a day in a prep course for the university and that was the subject. you made it so clear what they were talking about on the next day, thank you so much!!

This is an absolutely excellent explanation for Bezout's theorem! Thank you!

the greatest video of all time. watched 10 different videos on the same topic but they all have 1 thing in common, they dont tell you the real deal, they just assume you already know that 1 thing so they quickly brush it off. The whole underline as a variable thing is a game changer and what made me understand. Thank you.

Imagine a video, that is not intended to show, how to calculate the private exponent d in RSA with the extended euclidean algorithm, doing the best job of providing a step by step solution, with no holes or skips in it. Really good work! Your video is better than any RSA private exponent calculation video for understanding how the retreive d.

This was so much easier to understand than my textbook. Thanks a million!

Absolutely phenomenal explanation, goes over every little detail so you can't possibly feel lost at any one step. Couldn't for the life of me figure it out with the textbook or the other weird videos where they use a table and formulas that seemingly come out of nowhere, but this made it abundantly easy to understand. One watch and I could execute it flawlessly :)

I'm so lucky to find your video! It's clear and easy to understand. I'm struggling in my class. your video just saved my life!

The absolute bestest explanation I could find for this, THANK YOU!!

It works really well and the video was really well done! Having grown accustomed to a lot of algebra, calculus, trig, etc. its hard to start treating numbers like variables, but that made it click for me. However, I don't feel like the simplifying aspect was explained as well as it could have been, which is an extension of what I mentioned in the previous sentence. To clear things up: After each substitution, in order to simplify, distribute the co-efficient (if we're still thinking in terms of variables) to the lower value in each term. If it confuses you, just put both in parentheses, distribute to the smaller value, and re-write in ascending order on a new line. Also, yes, you need to simplify after each substitution, its too easy to lose track of where to distribute, and you'll probably mangle where you put your parentheses causing you to distribute improperly. Following this, we'll properly build up to the input values we used to compute our GCD originally. You should be able to simplify to a pair of numbers every time that make sense for your next substitution. If you don't follow this you'll probably get a garbage answer from making a mistake when simplifying. You can follow in the example below how its done. Example: Find s and t, where: 240s + 46t = gcd(240, 46) // Perform our GCD calculations gcd(240, 46) 240 = 46(5) + 10 46 = 10(4) + 6 10 = 6(1) + 4 6 = 4(1) + 2 4 = 2(2) + 0 // Re-writing according to the video (numbered for referencing): Equation 3: 240 - 46(5) = 10 Equation 2: 46 - 10(4) = 6 Equation 1: 10 - 6(1) = 4 Equation 0: 6 - 4(1) = 2

This was a great explanation. I don't think any other teacher tells you to treat those underlined numbers as variables. That was pretty helpful.

This was such a wonderful explanation. Straight to the point. I dig it

By far the best explanation iv seen on here, thank you so much John.

Excellent method John. I have watched many videos about it. But this is fantastic . Thanks

Had been confused my entire life with all these backward substitutionS. Thank you so much for this vid! It helped alot!

It's a shame we can't mark videos as the best solutions the same way we can do it on forums. This is definitely the best explanation on this topic.

This is the most beautifully explained video on this topic. Thank you so much!

Thanks! was stuck at this Algorithm for quite long, you explained it very well in just a few minutes.

Thank you, this is the best video on extended Euclidean!

Was a challenge to find a video or an article that would explain this algorithm in simple terms. Thank you!

This was an amazing learning video. Thank you so much for making it clear and concise!

This is the best and most clear explaination I have ever seen. Thank you so much.

My professor was speed running this algorithm in class, we covered it in like 10 mins. Thank you for the thorough explanation!

Thank you for providing this excellent explanation on how to use the extended Euclidian algorithm!

Incredible explanation. Way better than Zybooks.

At first I did not understand what my lecturer taught me in class but now I am happy to say i'll ace that exam....T hank you so much

Amazing video!! Clear, straight forward, and quick and I actually know what I'm doing now.

this video is awesome. makes the process completely understandable. thanks!

One of the best videos related to the topic, thank you sir.

Very good! Much easier than the formal explanation!!

Awesome video! The way you explained the methods are very precise and easy to understand, kudos to you. Thanks a bunch, you are making the world a better place! Cheers

thank you, this part was super confusing but it makes so much more sense now

absolutely great. it is amazing how great you explained that. GREAT WORK

The best explanation I've seen so far.

thank you so much! I literally spent so much time trying to figure out my homework problem but now through your video, I learned how to complete problems like these!

Thanks to you, many questions have been solved. Even though it's been a long time, you've been a good help.

very clear! been struggling with a problem like this and found your video!

Wow! I was struggling so much with the intuition and this finally made things click.

Thank you so much sir i watched multiple videos but everything was complicated and now this is my last video i don't need to watch anything else again thank you sir

this got me through my month-long class in like, a few days. Sooo good goddamn

Just brilliant, the variables was a game changer!

I have a final tomorrow and this just taught me so much- thank you!

i took help of many videos but they were out of my understanding. this video explained me very nicely thanks so much

Thank you so much, John! it's so easy to understand

one of the best math video i have seen in long time. thank you!

Thank you for the clear and concise explanation.

Excellent breakdown! Thank you!

Great explanation, very much appreciated!

Made super duper clear,thanks for creating such good contents

you made it so so easy! I have an exam tomorrow and I didn't think I would have time to understand it (since it looked so complicated) Thank you!

This has finally made sense, THANK YOU so much!! 🙏

The badass big rule nailed it 👌. Best explaination.. thank you so much

It all makes sense now. Thank you so much!

You explained it absolutely on point! Thank you!

This was super clear, thank you for this!

You taught me in 15 minutes, while my discrete professor couldn't even teach me this in a whole semester !!!!!!

Really easy to follow and understand, thanks so much

Beautifully Explained. Thank you.

Underline trick was amazing. Everything cleared out. I'd hope teachers like you [=that make thigns easy , and not teach jargon] had the seat of the teacher and not what is right now on my University.....

This was phenomenal! Thank you!

Thanks a ton. God bless you, your family and country :)

I asked my friends and watched so Many videos on youtube and still did not get it but thanks to u I get it now. thaankssss

Very clean and understandable. Thank you !

Best method of solving this. Every other video makes this so complicated.

Brilliant job Professor!

You made it so simple! Thanks a lot!

damn! so clear and straight to the point!!! thank you for this video!!

It is easy to understand from zero, thank you so much

Fantastic, very helpful video!

Really good explanation. Thanks a lot from India.

Best explanation I've watched on YT 🕺🏿 Thanks 🙂

very nicely put and clear video. thanks!

Found another underrated golden channel

What a legend! Best explanation.

I was having trouble with the back substitution but this helps, thanks.

I was so confused with this at school and ngl kind of struggling but this has helped so much

This is a perfect explanation, thank yoi very much!

the only egcd algorithm video that actually explains how to do it

thanks a mill! very well explained

Underline as variable! Thank you!

Great tutorial! Thanks a lot Master Teacher!

You taught this better than UC Berkeley. Thank you very much!

Thanks a lot for excellent explanation!!!

Is it complusary to place s with 56 and t with 15?, Cuz 56 is greater than 15, or something in bezouts theorem .

thank you - this couldn't have been clearer!!!

Thanks ! I had to adapt it to polynomials but works the same. Beautiful !

Thanks mate excellent explanation. My teacher just reversed it without explaining it.

Thank you so much for your help!!

Great video, very helpful!