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
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
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
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 a million for the super example and run-through! One question though, (anyone feel free to answer) I have this Q: 42x + 30y = 20. Putting into this: a = bq + r I get: 42 = 30(1) + 12... Correct? 30 = 12(2) + 6 12 = 6(2) + 0. Is 6 the GCD and is it that if 6 does not divide into 20, there are NO solutions? Please answer ASAP because my exam is on Monday ha, Thanks!
If you divide your original question by 2, you can get 21x + 15y = 10. Since the gcd of 21 and 15 is 3, which does *not* divide 10, then there should be no solutions. In essence, 21x + 15y will *always* be a multiple of 3, no matter the values chosen for x and y, and so that can never equal 10. I used this page as a reference: math.libretexts.org/Courses/Mount_Royal_University/MATH_2150%3A_Higher_Arithmetic/5%3A_Diophantine_Equations/5.1%3A_Linear_Diophantine_Equations I know your exam has long since passed, but I just came across this video and thought it would be neat to respond after such a long time has passed. I hope you have been doing well!
I came upon this video while working through your channel's playlist on Number Theory. Where is the "earlier video" referred to at 0:40? It's not in the playlist, at least not before this one. Is it the one from the axiom channel that actually follows this one in the playlist. That one is at th-cam.com/video/7pAyqUvJqzA/w-d-xo.html .
join our axioms newsletter to learn about new number theory videos: news.axioms.com/join
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.
This was only video in whole you tube having 100k+ views of diophantine equation
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
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 .
2:54 that's the important part
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. :)
That's wonderful to hear! We're so glad you found our video helpful.
this is the best and most easy to understand tutorial i have come across about Diophantine equations
I love Diophantine equation!!!❤❤❤
Maths can be hard but it can be fun sometimes!😊
Thank you! Good luck in your Discrete Math course, and we hope to resume making math videos very soon.
Dude.
@@glebanych2000 ikr
This is a great video rather than hand writing from some of the similar videos. Thanks for making it interesting and 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 ~
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!
@theredgear12 Thank you for your compliments! I'm very glad you found it useful.
0:45 I can't find the earlier video on single variable eqn. Where are they??
I am so happy to find this channel on TH-cam.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
anyone noticed he has written his channel's name in greek letters on top left corner amazing work though
hi gan,how to find all solution from diophantine equation if we have been find the one solution??
Thank u very much i was not getting it for a very long time but now understood it finally😉
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.
@ironman236 My apologies - we are running a bit behind. We hope to resume making math videos in a few weeks.
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! :)
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..
Thank you so much sir, I now understand this , more grace
Finally it's clear... 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.
This video was Diophantastic!
im trying to test out of algebra 2, this helps so much thank you
I'm very grateful for the video you put here, because its very interesting!!!!!!!!
Thank you so much for sharing us. God bles
First class explaination
Very helpful video. Thanks a lot!!
Could you please tell me which software are you using for writing.
thank you so much sir it's very helpful for me in my finals thanks alot
You were of great help. Thank you!
Brilliant Video helped a lot !! What software do you use for typing the maths ?
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
How to find general solution of linear diophantine equations
Really like the style of this video :)
Next video? Where can I find other videos on number theory by you?
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
Wonderfull explanation..
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!
Thanks. It is a very good video. Please continue.
The best video, thank you 🙂
Is there any way we can get the script? As in what you typed in the video?
which software are you using? Great video by the way :)
Thanks from ,,,🇮🇳🇮🇳🇮🇳🇮🇳🇮🇳
Thank you this is very well explained good job!
Still a gem!
Sir, suppose we have a gcd(1,4) = 1 , how can we write it as a linear combination.
Your videos are very helpful. Thank you :)
Thanks a lot. Excellent explanation.
Thanks man, really helped!
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
dude your awesome. i just subscribed!!!
thanks , please solution the question
determine gcd (9999,990) by the euclidean algorithm.what is the value of lcm(9999,990) ?
Thanks from India
Very interesting subject and great class! Thank you socratica
well explained thank you!
Sir will you please tell me the name of the software you are using.
This is so good ..... Wow 💕
How about 35x + 14y = 91, it equals not to 1? Can it be solved using diophantine equation?
I’m still currently watching the video, but how is this concept different from bèzouts identity?
Excellent video!
it's simply the linear combination between 47 and 30 which we studied in class 10th
What if one of the coefficients a or b is 1?
Is there a way to use the Euclidean algorithm to obtain positive integer solutions for x and y only?
omg life saver, thank you so much!
If gcd (a,b)=1 then how to prove gcd (a^2 , b^2) =1?
thank you bratan
Very thank you respected sir....
How to solve 3 variable Diophantine eqn?
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 u❤
thanks for the awesome video!
Please post the next video!
Never happened.
you are awesome I understood everything thank you
i can't use the steps you did on 2x + 3y = 0
isn't that the same as bezouts identity?
What to do if, we don't get the remainder 1 and instead get 0
@@shivamjoshi7047 gcd will be the above remainder
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.
Good
Thanks for done
Thanks a million for the super example and run-through!
One question though, (anyone feel free to answer)
I have this Q: 42x + 30y = 20.
Putting into this: a = bq + r I get:
42 = 30(1) + 12... Correct?
30 = 12(2) + 6
12 = 6(2) + 0.
Is 6 the GCD and is it that if 6 does not divide into 20, there are NO solutions?
Please answer ASAP because my exam is on Monday ha, Thanks!
If you divide your original question by 2, you can get 21x + 15y = 10. Since the gcd of 21 and 15 is 3, which does *not* divide 10, then there should be no solutions. In essence, 21x + 15y will *always* be a multiple of 3, no matter the values chosen for x and y, and so that can never equal 10. I used this page as a reference:
math.libretexts.org/Courses/Mount_Royal_University/MATH_2150%3A_Higher_Arithmetic/5%3A_Diophantine_Equations/5.1%3A_Linear_Diophantine_Equations
I know your exam has long since passed, but I just came across this video and thought it would be neat to respond after such a long time has passed. I hope you have been doing well!
Thank you!
I came upon this video while working through your channel's playlist on Number Theory. Where is the "earlier video" referred to at 0:40? It's not in the playlist, at least not before this one. Is it the one from the axiom channel that actually follows this one in the playlist. That one is at th-cam.com/video/7pAyqUvJqzA/w-d-xo.html .
Really helpful
Never been so easy
Awesome!
THANK YOU SO MUCH, SIR. REGARDS VIKRAMJIT PAUL