I'm honestly amazed how helpful many math videos on youtube can be. 5 years ago, I would have never understood dual spaces if it wasn't for a youtube video. Now, this jem.
I CANNOT thank you enough for this! I have a maths exam coming up and my teacher rushed through this topic so I was completely lost but now it makes so much more sense!
You know why i haven't fallen i love with math for ages , because i haven't had a cool teacher like you , nice work mate ... i am lazy enough not to put any comment on youtube ..But you made me to do to appreciate your video ... thanks for tutorial
Thank you so much. I'm having Discrete Mathematics and our professor discussed this yesterday and I only got confused but now I understand this topic because you explain much better compared to our professor. Thanks again.
Thanks for this video! I took a Number Theory class a few years ago and absolutely loved it. Now that I have graduated, I have been occasionally flipping through that class's textbook to refresh/relearn that information. This video was much more helpful than seeing the whole process written out in a textbook!
Great channel, very informative videos! You guys can explain in 10 minutes what most of my professors can't in 2 hour sessions. Just a little note, Socratica in Greek is "Σωκρατικα" :)
Hi, thanks for making this video. I am working on an assignment wherein I have to do exactly this process and was not understanding it the way my professor/the textbook explained it. I worked on one of my own problems during your video and ended up with an acceptable solution. You've made my night. :)
Nice video! But please, just a couple more examples! I figured out that for the integers 56 and 32, 56x + 32y = 8, if x = -1 and y = 2. But I'm not sure how I did it! I mean I sort of get the algorithm, but there was some guessing and checking going on along the way. So I'm still not 100% comfortable with the algorithm. PLEASE just a couple more examples!!!! If you do, I promise to buy you a beer, coffee, or any beverage you like!
thank you so much for this video! i'm trying to solve for a similar problem. I haven't taken number theory yet, but this make so much sense and has saved my life to say the least...thanks again! :)
***** That's obvious, just take the initial y and add 47t (where t is a variable integer) and subtract 30t from the initial x. This means that the coefficients of t are getting cancelled, and we are left with the original Diophantine.
can you apply diophantine equation to balance chemical equations? i am a little confused how to apply it in the field of chemistry. i am currently working for my exposition fo the final output pleeaseeee help us out. thanks a lot po
A much faster way: 47x = 1 mod 30 -13x = 1 mod 30 This leads to a reduced problem -13x = 1 + 30k 30k = -1 mod 13 4k = -1 mod 13 k = 3 Substituting k back into the reduced problem gives --13x = 1 + 30*3 x =-7 Substituting x = -7 in the original equation gives y = 11. So the parameterized solution is x = -7 + 30k y = 11 - 47k
here’s my proposal for finding the other solutions (at least some of them): if you look at the final equation 30(11) + 47(-7) you can see that if you add or subtract 47 from 11 and then do the opposite for -7 with 30, it works out. so for example 30(11-47)+47(-7+30)= 30(11)+47(-7)-(47)(30)+(47)(30)=1+0=1 so 11-47=-36 and -7+30=23 are also a solution
Terrific video, as with all the other commentators, I would like to know what software was used in this video. Thank you very much for such a clear explanation.
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Hi, loved your video, where can i find the video where you explain how to find all the possible integer solutions using this method? Thank you : D
I'm honestly amazed how helpful many math videos on youtube can be. 5 years ago, I would have never understood dual spaces if it wasn't for a youtube video.
Now, this jem.
I CANNOT thank you enough for this! I have a maths exam coming up and my teacher rushed through this topic so I was completely lost but now it makes so much more sense!
You know why i haven't fallen i love with math for ages , because i haven't had a cool teacher like you , nice work mate ... i am lazy enough not to put any comment on youtube ..But you made me to do to appreciate your video ... thanks for tutorial
Thank you so much. I'm having Discrete Mathematics and our professor discussed this yesterday and I only got confused but now I understand this topic because you explain much better compared to our professor. Thanks again.
This was only video in whole you tube having 100k+ views of diophantine equation
Hats off to the guy explaining such an tough concept in an easy way in 10 mins but such an easy, short and detailed explanation .
Thanks for this video! I took a Number Theory class a few years ago and absolutely loved it. Now that I have graduated, I have been occasionally flipping through that class's textbook to refresh/relearn that information. This video was much more helpful than seeing the whole process written out in a textbook!
this is the best and most easy to understand tutorial i have come across about Diophantine equations
Great channel, very informative videos! You guys can explain in 10 minutes what most of my professors can't in 2 hour sessions. Just a little note, Socratica in Greek is "Σωκρατικα" :)
2:54 that's the important part
Hi, thanks for making this video. I am working on an assignment wherein I have to do exactly this process and was not understanding it the way my professor/the textbook explained it. I worked on one of my own problems during your video and ended up with an acceptable solution. You've made my night. :)
That's wonderful to hear! We're so glad you found our video helpful.
I love Diophantine equation!!!❤❤❤
Maths can be hard but it can be fun sometimes!😊
This is a great video rather than hand writing from some of the similar videos. Thanks for making it interesting and useful!!
@theredgear12 Thank you for your compliments! I'm very glad you found it useful.
Thank you so much! This was awesome, nobody is as patient as a video :)
Woww !! Such a great explanation.. This really helps me in my study, so THANK YOU SO MUCH !!! Keep it up ~
The way you teach is amazing and so it is easily understood. Bravo!
Thank you for breaking down the long process, so I can better understand how to shorten with matrices.
I am so happy to find this channel on RUclips.You are doing a great job...Thank you for teaching us...This video helped me in my discrete math test...
We're so glad you found us!! Let us know how you get on...
i was just trying to find a good video on diophantine equation and i found you
Thank you! Good luck in your Discrete Math course, and we hope to resume making math videos very soon.
Dude.
@@glebanych2000 ikr
0:45 I can't find the earlier video on single variable eqn. Where are they??
@ironman236 My apologies - we are running a bit behind. We hope to resume making math videos in a few weeks.
Nice video! But please, just a couple more examples! I figured out that for the integers 56 and 32, 56x + 32y = 8, if x = -1 and y = 2. But I'm not sure how I did it! I mean I sort of get the algorithm, but there was some guessing and checking going on along the way. So I'm still not 100% comfortable with the algorithm. PLEASE just a couple more examples!!!! If you do, I promise to buy you a beer, coffee, or any beverage you like!
Thank u very much i was not getting it for a very long time but now understood it finally😉
Please I would love to see the next video on Diophantine equations :O
You do an exceptional job of explaining.
Tysm ...uh helped me out so easily ....
thank you so much for this video! i'm trying to solve for a similar problem. I haven't taken number theory yet, but this make so much sense and has saved my life to say the least...thanks again! :)
hi gan,how to find all solution from diophantine equation if we have been find the one solution??
Thank you so much sir, I now understand this , more grace
anyone noticed he has written his channel's name in greek letters on top left corner amazing work though
Finally it's clear... thank you
Very helpful video. Thanks a lot!!
I'm very grateful for the video you put here, because its very interesting!!!!!!!!
Did you ever release the next video? Would like to know how to get all the solutions?
***** That's obvious, just take the initial y and add 47t (where t is a variable integer) and subtract 30t from the initial x. This means that the coefficients of t are getting cancelled, and we are left with the original Diophantine.
+Spandan Bhattacharya Well apparently it isn't obvious, is it?
Jullix993 Sorry for being an asshole, I was too caffinated when I put in that comment.
Spandan Bhattacharya Been there!
0:45 I can't find the previous videos on single variable..
This video was Diophantastic!
Thank you so much for sharing us. God bles
You were of great help. Thank you!
thank you so much sir it's very helpful for me in my finals thanks alot
Thanks. It is a very good video. Please continue.
Could you please tell me which software are you using for writing.
Wonderfull explanation..
Thanks a lot. Excellent explanation.
Next video? Where can I find other videos on number theory by you?
First class explaination
Really like the style of this video :)
Still a gem!
This was really very well done and explained! Thank u very much, Sir. Please accept my best regards.
This was really helpful, thank you so much!
The best video, thank you 🙂
im trying to test out of algebra 2, this helps so much thank you
How to find general solution of linear diophantine equations
Thanks from India
Thank you this is very well explained good job!
well explained thank you!
can you apply diophantine equation to balance chemical equations? i am a little confused how to apply it in the field of chemistry. i am currently working for my exposition fo the final output pleeaseeee help us out. thanks a lot po
That's Linear Algebra. You're looking for Gaussian Elimination.
Sir, suppose we have a gcd(1,4) = 1 , how can we write it as a linear combination.
Excellent video!
thanks , please solution the question
determine gcd (9999,990) by the euclidean algorithm.what is the value of lcm(9999,990) ?
Is there any way we can get the script? As in what you typed in the video?
thank you bratan
This is so good ..... Wow 💕
How about 35x + 14y = 91, it equals not to 1? Can it be solved using diophantine equation?
Very interesting subject and great class! Thank you socratica
How to solve 3 variable Diophantine eqn?
omg life saver, thank you so much!
Thanks from ,,,🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳
A much faster way:
47x = 1 mod 30
-13x = 1 mod 30
This leads to a reduced problem
-13x = 1 + 30k
30k = -1 mod 13
4k = -1 mod 13
k = 3
Substituting k back into the reduced problem gives
--13x = 1 + 30*3
x =-7
Substituting x = -7 in the original equation gives y = 11. So the parameterized solution is
x = -7 + 30k
y = 11 - 47k
Thanks man, really helped!
here’s my proposal for finding the other solutions (at least some of them): if you look at the final equation 30(11) + 47(-7) you can see that if you add or subtract 47 from 11 and then do the opposite for -7 with 30, it works out. so for example 30(11-47)+47(-7+30)= 30(11)+47(-7)-(47)(30)+(47)(30)=1+0=1 so 11-47=-36 and -7+30=23 are also a solution
I’m still currently watching the video, but how is this concept different from bèzouts identity?
Your videos are very helpful. Thank you :)
Thank u❤
thank you a lot for this video it helped me very much i really appreciate that, keep up the good work and much much thanks
Thanks for done
Is there a way to use the Euclidean algorithm to obtain positive integer solutions for x and y only?
Sir will you please tell me the name of the software you are using.
What if one of the coefficients a or b is 1?
thanks for the awesome video!
which software are you using? Great video by the way :)
Brilliant Video helped a lot !! What software do you use for typing the maths ?
Very thank you respected sir....
dude your awesome. i just subscribed!!!
what is the difference between this and bezout identity?
Thank you for pointing that out; I think this example is demonstrating Bezout's identity!
Thank you!
you are awesome I understood everything thank you
If gcd (a,b)=1 then how to prove gcd (a^2 , b^2) =1?
Really helpful
it's simply the linear combination between 47 and 30 which we studied in class 10th
isn't that the same as bezouts identity?
Awesome!
i can't use the steps you did on 2x + 3y = 0
Thank you so much
beautiful!
AMAZING
What to do if, we don't get the remainder 1 and instead get 0
Please post the next video!
Never happened.
Terrific video, as with all the other commentators, I would like to know what software was used in this video. Thank you very much for such a clear explanation.
Thanks bro😊
Thanks❤🙏