Bézout's identity: ax+by=gcd(a,b)

Подписаться 1,3 млн

Просмотров 78 тыс.

50% 1

Check out Max! Proof of the Division Algorithm, • Natural Numbers 1.3 Di...
Bézout's identity, ax+by=gcd(a,b),
Euclid's algorithm, zigzag division, Extended Euclidean
number theory playlist: • Playlist
💪 Join our channel membership (for as low as $0.99 per month) to unlock several perks, including special badges and emojis during the livestreams: / @blackpenredpen
🏬 Shop math t-shirt & hoodies: teespring.com/stores/blackpen...
10% off with the code "TEESPRINGWELCOME10"
Equipment:
👉 Expo Markers (black, red, blue): amzn.to/2T3ijqW
👉 The whiteboard: amzn.to/2R38KX7
👉 Ultimate Integrals On Your Wall: teespring.com/calc-2-integral...
---------------------------------------------------------------------------------------------------

Опубликовано:

24 апр 2018

Ссылка:

Скачать:

Готовим ссылку...

Добавить в:

Мой плейлист

Посмотреть позже

Комментарии : 120

@wobblyjelly345 3 года назад

You explain this so well and the only example I have found that I can actually follow, thank you! 😊

@halik919 3 года назад

I was lazy and didn't want to watch an 18 minute video! Now, I am more than grateful I clicked and watched. Thank you, best explanation ever!

@pablosabogal5132 3 месяца назад

Thank you for your upbeat atittude that made me feel a lot better!

@wajdefadool3459 2 года назад

BIG Thanks man your videos helps a lot as a collage student

@khoaang5712 2 года назад

Thank you for your explanation, it helps my report so much. And I really like your smile. Thank you

@blackpenredpen 2 года назад

😃

@mzoon6823 5 лет назад

Thank you man, this is so useful

@chloinger Год назад

This was the best explanation ever! Thank you! You saved my maths exam. :)

@tejadamichelle4889 3 года назад

Thank you for a very nice explaination. Keep it up 🙂

@abd-elrahmanmohamed9839 6 лет назад

Nice as usual ! thanks!

@MathForLife 6 лет назад

Nice!! My favorite part is quantifiers "forall" and "exists":D

@blackpenredpen 6 лет назад

Eightc yay!

@luissalvador6711 2 года назад

instaBlaster...

@stanleygondwe6859 Месяц назад

Excellent explaination

@maaikevreugdemaker9210 22 часа назад

It feels so weird to have done calculus without having learned this stuff.. thanks!

@shrameesrivastav1130 6 месяцев назад

Damn, this is flipping awesome explanation! ♥

@lilianavalente1385 3 месяца назад

Thank you, you explained it so well that I am confident in passing my discrete maths exam

@NeelSandellISAWESOME 3 года назад

nice, i didn't know about the lcm trick. Thanks

@tarunsingh7243 Год назад

Amazing explanation 👌👌

@rohitg1529 6 лет назад

Can you please make a video about why Euclid’s algorithm finds the GCD? We were taught how to do this in the 6th grade I think, but I never thought about why it works until now.

@sharonjuniorchess 4 года назад

This might help medium.com/i-math/why-does-the-euclidean-algorithm-work-aaf43bd3288e

@Magic73805 6 лет назад

Thank You vey much. Sir.

@blackpenredpen 6 лет назад

Yay!

@NotYourAverageNothing 6 лет назад

I have a few suggestions for videos. Here’s just one: Two circles of radius R intersect each at exactly two points. Lines are drawn from each of those points to the center of one of the circles. Those lines and the inner arc of the other circle define a region. What is its maximum area?

@NotYourAverageNothing 6 лет назад

Shree Ganesh I don’t know the answer with 100% certainty, but… …I think (going off of memory here) it’s (-πR^2 + R√3)/6.

@chronicsnail6675 3 года назад

this is better than the resources my uni has thanks

@fadirached2247 3 года назад

Very helpful!!

@doodelay 4 года назад

damn this was a really clever solution, props to bezout!

@PhilBoswell 6 лет назад

The Number Theory playlist in the description contains a private video at #4: I have watched all the others so what am I missing?

@psrs985 2 года назад

Woah!! Wonderful explination Love from indiaa💗

@x15cyberrush9 5 лет назад

thank you black pen red pen

@1234Daan4321 6 лет назад

Why do x and y have to be integers? If you fill in complex numbers for m they cancel out as well, right?

@patipateeke 6 лет назад

Thanks!

@srpenguinbr 6 лет назад

Amazing!

@jacksonsingh855 6 лет назад

Please do a videos on how to find inverse of a function

@112BALAGE112 6 лет назад

If you can't solve the equation y=f(x) for x then use: en.wikipedia.org/wiki/Lagrange_inversion_theorem

@shacharh5470 6 лет назад

Cool fact: Bezout's lemma (that's how I learned it) is actually applcable in any group that's similar enough to Z. I learned a general form of the lemma in a course on group theory. Of course in group theory the notions of gcs and lcm are defined more generally in terms of subgroups and their generating sets. Interesting stuff if you're into that sort of thing.

@alkankondo89 6 лет назад

That's cool! I have taken a course on group theory but have not heard of Bezout's Lemma. I'll have to look more into that.

@mattgsm 6 лет назад

What do the pen colours represent? Is the black colour to do with the original question while red is an insertion or something?

@ShahriarNafiz50 9 месяцев назад

Awesome!!!

@kantaprasadsinha8025 3 года назад

Thank u. U may arrange a video on Bezout identity and Uclid Algorithm.

@azzteke 2 года назад

EUCLID please!

@jameshenner5831 6 лет назад

Hey Blackpenredpen, do a video on the (complex valued) infinite series Sum(i^(n-1)/n) from n = 1 to infinity.

@mashroom2927 3 месяца назад

8:57 this reminds me of finding the multiplicative inverse in ciphering class

@halanasser5589 5 лет назад

How to use it if a+b is the exponent and thier gcd(a,b)=1 ??

@benjaminbrady2385 5 лет назад

Do the numbers on the side of Euclid’s algorithm always multiply to also give you the gcd or is that a coincidence

@elie.makdissi 3 года назад

ikr i noticed that also

@pamameh1841 4 года назад

Don't the possible values for Y have to be in the range 0 to (n-1) in our case 0 to (432-1)? ie 7 +432 = 439 but that's greater than 432. so only one solution?

@BigDBrian 6 лет назад

11:45 "I will call this x naught and y naught because why not" is what you should've said! you missed a pun opportunity. I'm disappointed.

@yosafendrafendra7960 6 лет назад

Hei I really like your posts!! but i have a question for you bout 3D topic. ABCD.EFGH Cube, its side is a. Point O is intersection between AC and BD. Determine the distance between line EO and line HB..please answer thiss

@edslab5383 2 года назад

Great!

@dariushuang1115 2 года назад

for people unfamiliar with the Euclid's Algorithm, it's actually based upon the lemma: Suppose b = aq + r, then gcd(a, b) = gcd(a, r). You can prove this lemma by contradiction in ~8 lines

@mjones207 6 лет назад

I was so hoping at 11:43 for "I will call this x-naught and y-naught because... why not?"

@blackpenredpen 6 лет назад

mjones207 oh... I should have done that. :)

@gdudhdydhsudjdu6350 7 месяцев назад

How can we prove the validity of a theorem with a single example?

@sharpnova2 2 года назад

I haven't watched this video yet but just judging from the very first statement you wrote at the beginning isn't this just the extended euclidean algorithm

@General12th 6 лет назад

Should I multiply it out?

@joanlegada5370 3 года назад

so the final x is -2+7m and final y is 7-24 m?? :)

@sergiogarofoli573 4 года назад

I have an issue here: After Bézout's identity, ax+by=gcd(a,b), My problem is such as "ax" is known N and "by" is the unknown from the type [-(x-1)*gcd(a,b)] and of course gcd(a,b) is the unknown I'm looking for.

@znarwhal4530 6 лет назад

What does the upside-down A and the backwards E mean?

@benplayzgames1 6 лет назад

AddQ he literally said it in the video

@vanessakitty8867 6 лет назад

For All and There Exists

@SleepyRickyC92 6 лет назад

AddQ Quantifiers. You will encounter it in a discrete math or logic course.

@sahhaf1234 4 года назад

Superb..

@alandaniels2095 2 года назад

Why does he have ball in his hands?

@chronicsnail6675 3 года назад

whats so important about bezouts indentity

@sutgdi749 25 дней назад

why he holding that black ball ?

@riteshrastogi5388 5 лет назад

there is also a blue pen LOL : )

@mihaipuiu6231 2 года назад

Dear prof. Blackpenredpen...you are very good speaker,,...your problems are very interesting, but..please...your carioca is writing sometimes, hard for me to read symbols. Can you improve this symbol's visibility?

@yousefalyousef59 3 года назад

let: 1/(a-b)(a+b)=A/(a+b)+B/(a-b) and form it ■A(a-b)+B(a+b)=1 ■a(B+A)+b(B-A)=1 Here are two cases of a Bezout's Lemma. say some thing about that.

@siggelicious4485 Год назад

fucking genius

@stevengottlieb6023 6 лет назад

I am sorry, but you did not show that ALL solutions are in the form x=-2+7m and y=7-24m. In theory there can be other solutions then the ones you showed.

@blackpenredpen 6 лет назад

Steven Gottlieb I agree with you. But I was just showing an example on how this works. Notice the video is 18 minutes already. Max or I will work out the proof for that in the future on another video.

@NotYourAverageNothing 6 лет назад

blackpenredpen Can you plz prove that Bézout Coefficients are not unique? Are there any numbers were there *_are_* unique?

@NotYourAverageNothing 6 лет назад

Steven Gottlieb It does give every solution, unless m is restricted to integers.

@stevengottlieb6023 6 лет назад

Thank you for responding!

@stevengottlieb6023 6 лет назад

Yes, every solution was given. The problem is that was not proven. Even BPRP agrees with that.

@Abohafsah 4 года назад

Change your lighting system, board can’t be seen easily

@jiajunxu614 2 года назад

proof is more difficult than application

@stanleygondwe6859 Месяц назад

❤❤❤

@RealtyTaj Год назад

@4:41 you had a mistake the gcd(436, 126) = 2

@enginermis4626 9 месяцев назад

wtf

@kantaprasadsinha8025 3 года назад

One thing is peculiar. Upto 1960 agebra books, there was no word Euclidean algorithm,a term for determining G.C. D. All are forced to swallow this coinage.Again, Bezout' s identity is renamed as Extended Euclidean Algorithm . This is cultural imperialism.as if no civilisation did not think GCD or HCF

@OonHan 6 лет назад

Hi!

@maxhaibara8828 6 лет назад

Bezout Identity? I thought the name is Extended Euclidean

@shacharh5470 6 лет назад

It's not an identity, I don't know why he calls it that. It's an existence claim so clearly not an identity. As for the name, I've learned it as "Bezout's lemma", there's a version of it for integers, a version of it for polynomials and a generalized version of it for groups

@sugarfrosted2005 6 лет назад

The extended Euclidean ALGORITHM is how you find the integers x and y in Euclidean domains (such as the integers). The Bezout identity is the resulting equation. There are mathematical structures where such x and y exist, but even the normal Euclidean algorithm doesn't work. As a general rule, the result isn't the algorithm.

@sugarfrosted2005 6 лет назад

Shachar H Wikipedia calls it the Bezout identity and I think I've heard that term used in Bezout domians (things where the x and y always exist).

@eleazaralmazan4089 6 лет назад

Both Bezout's Identity and Bezout's Lemma are correct.

@makshudulislam7442 4 года назад

We want more IMO Problem

@sharonjuniorchess 4 года назад

Question: A dealer bought a number of horses at $344.00 each, and a number of bullocks at $265.00 each. He then discovered that the horses had cost him in all $33.00 more than the bullocks. Now, what is the smallest number of each that he must have bought? [Source: 536 Puzzles by Dudeney #20]

@chronicsnail6675 3 года назад

your way of finding gcd is better than text book

@worsethanjoerogan8061 3 года назад

It's technically the same way, but I agree that writing it out in that equation style is confusing as hell

@eipiwau 6 лет назад

You are calling it y naught because why not xD

@matteovitellaro1082 3 года назад

I love you

@DeViLTh0rn 5 лет назад

“Because we are know we are smart, don’t do that “ 😂😂😂

@manu_j_ 6 лет назад

9:02 something magic happened

@mathematicstvc6000 6 лет назад

Hello

@Anteater23 6 лет назад

Did my 'Calc 3' paper today. Was nervous and made a couple stupid errors and I didn't get a couple of things but on the whole it went ok. One mistake was 4r^4 x 0 x 0 = 4r^4

@blackloop1861 6 лет назад

Can you do a video about 1+2+3+4....=-1/12

@BigDBrian 6 лет назад

mathologer

@FlexThoseMuscles 8 месяцев назад

whohoo solved

@john-athancrow4169 6 лет назад

WHY A.L. AGAIN!!!!!!!!!!

@blackpenredpen 6 лет назад

Ιωάννης - Αθανάσιος Χαραλάμπους What's AL?

@kenichimori8533 6 лет назад

Ensemble theory d(^^)

@eliascaeiro5439 6 лет назад

0:19 "Okay in this video I'm going to demonstrate one of the most useful facts in number theory." but you didn't prove anything, you just showed an example. Honestly I must say I'm a bit disappointed with your videos lately. Anyway, it's just what I think so don't let it bother you.