A Nice Diophantine Equation in Number Theory | You Should Learn This Theorem | Math Olympiad

Subscribe to my new channel at
youtube.com/@PKMath1234?si=SI...
Videos will now be uploaded in my new channel.
In this video, I am introducing a nice diophantine equation in number theory and also a wonderful theorem you can use to solve a linear diophantine equation with two unknown variables. With this theorem, most of the linear diophantine equations with two unknown variables will be nicely solved. Diophantine equation is an interesting topic in number theory. Come check this video out and watch it until the end. This would also be a good practice for math olympiad. More with diophantine equation problems will come! Stay tuned!
💬 Did you enjoy this video? Tell me all about it in the comment section below!
Subscribe to Dr. PK Math here ⤵️
kzbin.info?su...
*************
✅ Follow Modern Dr PK Math on social media:
Instagram ▶️ / drpkmath1234
Facebook ▶️ / drpkmath
Twitter ▶️ / drpkmath
*************
#DrPKMath #diophantineequation #matholympiad

[@devondevon4366]

22y + 57x =400 ~ this will use for congruent to 0y + 13x `~ 4 ( mod 22) 13 x ~26 (mod 22) x ~ 2 (mod 22) x = 2 + 22k equation A Since 22y + 57x =400 ,then 22y + 57 ( 2+22k) =400 22y + 114 + (57)(22k) =400 22y = 286 - (57)(22k) y = 13- 57k equation B when k= 1 , x = 2+22 = 24 and when k=1 , y = 13-57 = -44 So one solution is (24 - 44) let's plug in these values in the original equation, 22y + 57k=400 22(-44) + 57(24) = 400 -968 + 1368 =400 400 = 400 Trying other values when k=2 x= 2+ 44 = 46 and y= 13-114 = - 101 let's plug in 46 and - 101 into the original equation (22)(-101) + 57(46 = 400 -2,222 + 2622 = 400 400 = 400 So, the solution for the linear diophantine equation 57x + 22y =400 is x= 2+22k, and y =13-57k

[@pkmath12345]

Nice work! Thanks for sharing your work Devon👍👍👍

[@MrGLA-zs8xt]

Ingenious method. thank you for your dazzling explanation sir

[@pkmath12345]

Thank you my man👍👍👍

[@sarahsiddiqui361]

Sir here how did you wrote it, explanation please 4:59

[@domedebali632]

Very nice sir. Muchas gracias

[@pkmath12345]

De nada haha👍👍👍

[@iiwacky6480]

i found x=22k+12 and y=(-627k-142)/11 using modular arithmetic

[@pkmath12345]

Nice work! Thanks for sharing my friend👍👍👍

[@pythona-z7052]

X=2-22k Y=13+57k

[@pkmath12345]

Come to my new channel friend!

[@clasher9667]

Thank you sir

[@pkmath12345]

Come to my new channel my friend👍👍👍

[@Mathstoon]

Nice technique!

[@pkmath12345]

Thank you for your comment mate👍👍👍

[@Mathstoon]

@@pkmath12345 You are most welcome!

[@Crazy_mathematics]

A= { a | 0 < a < 1 } Therefore n(A) = ∞

[@pkmath12345]

Thats right sir haha👍👍👍

[@Crazy_mathematics]

@@pkmath12345 can you prove sir how it is ?

[@swetabanerjee5213]

How to find value of n?

[@Bluebirdgirl]

Heyy sir i am From India 🇮🇳... (Kerala) Nice class🎉🙌

[@pkmath12345]

Hello my friend! Come to my new channel! Link is in the comminity tab👍👍👍

[@Bluebirdgirl]

@@pkmath12345 hey how are u sir

[@pkmath12345]

@@Bluebirdgirl Hey how are you? Did you subscribe to my new channel?

[@barryjackson405]

X=2,y=13

[@pkmath12345]

Nice👍👍👍

[@robbel3819]

What is "n"?

[@juldegorio2970]

"n" is any integer.

[@Min-cv7nt]

I am the first today

[@pkmath12345]

Thank you my friend👍👍👍

[@arunachalamhariharan9082]

This method is just too much use of higher mathematics . I use only school level ( 8th class level ) mathematics to solve such simple problems . The core of my thinking is 400 = ( 7 × 57 ) + 1 & ( 57 × n ) + 1 = 22 × p Finding n and p is a school level thinking . My request PLEASE DO NOT COMPLICATE SIMPLE SCHOOL LEVEL THINKING . THIS WILL KILL INVENTIVE THINKING . Thanks .

[@pkmath12345]

Thats why you failed to find general solutions for this question. Nothing really complicated and Ive given out a simple formula you can use to come up with general solutions for linear diophantine equation. Not every math can be done with 8th grade level math bro. If you are not enough, right attitude is to LEARN and not complain anything as it is from your lack of understanding. Inventive thinking is something people like you should not be mentioning or just be quiet