Chinese Remainder Theorem 

I have "learned" this in 3 different classes, and this is by far and a way the most intuitive and well reasoned explanation I have come across for doing the calculation. I come from a pure math background so the professors have all tried to give a quotient group or ring argument then hand wave away the calculation.

These comments thanking you are NOT overstatements. This was a wonderful explanation, sending my thanks from college

This is so simple, and every resource I've come across makes it look so difficult.... "Simplicity is the Ultimate Sophistication" many thanks!

I can't help but cry after understanding this. You are a life saver and relieves me from false assumptions that my brain ain't working anymore.

Number theory is my favorite discrete math branch. Although, when I assume that I have mastered a technique, something worse is waiting for me in the corner. Thank you from the deepest of my heart. You have made this complex theorem ridiculously easy. "There are three components to success: simplify, simplify simplify."

I needed to review the CRT when one of my students presented me with this problem: "Find digits X,Y,and Z so that the number 789,XYZ is divisible by 7, 8, and 9, where X, Y, and Z are in {0,1,2,3,4,5,6}." This example has the *perfect* blend of a concrete example with just the right amount of theory/algorithm (x,b,i,N,etc), along with narration that is not unpleasant to listen to. Thank you so much!

Very well explained - thank you! It's rare to find this kind of high quality tutorials (for free).

Finally explanation that makes the concept easy rather than making it more complicated ,I seriously can't thank you enough 💜💜

Never seen better presentation skills and organization. People, of course, can take a few shortcuts on an exam with time constraints. Thank you!

Thx a lot!!!! This is the simplest way to think of CRT I have learnt so far. Really helpful for my final

I want to cry at how much you saved me. I've been trying to understand this unit for the past 2 days. This 13 min video helped me more than everything I have trie so far. I am literally in tears while I am writing this comment. THANK YOU SO MUCH!!!!!!

Thanks a lot.I am a teacher of Further Mathematics in Cameroon and I find your tuts very helpful!!

Came here from Advent of Code 2020 - Day 13

The BEST and most clear explanation I've seen of this. I finally understand, thank you!!

Thank you so much for this, I have been having so much trouble understanding this and this video has made it so easy to understand.

That is THE best explanation I've seen for this. Thank you, this has helped me a lot and I don't think I'll ever forget this easy way of solving it. Thanks!

Thank you so much, this was really helpful! I'm a third year maths undergraduate and have always struggled with the Chinese Remainder Theorem from the moment we learned it in Abstract Algebra in first year, but will definitely be using this method from now on. I have a number theory exam in two days so fingers crossed this helps! ^.^

Mrs Jay I cannot express how much you have saved my life. I am now an absolute tank at these, I am moving to Beijing as we speak.

RSA is the Most beautiful application of Mathematics ever devised. It is simple yet so powerful that it gives people sleepless nights.

I hadn't get the concept so clear like this in youtube. Thank u

Thank you so much! everything I looked at made it look so hard. your explanation is great and simple!

Thank you for going through all the steps no matter how simple. It made it very easy to follow.

The best CRT explanation I have seen all over the internet ...Thank you so much ❤️

Clear and precise, really loved the explanation and the checking methods

When I searched "Chinese Remainder Theorem" on RU-vid, this video is by far the easiest to understand. Thank you!

Without a doubt the best explanation I’ve seen!! You are awesome..thank you you’re a wonderful teacher!

This was a great explanation. I keep forgetting how to do this, but your explanation is very intuitive!

Very simple and clear explanation. Much appreciated !

Well explained! It's videos like this that make RU-vid such a fantastic resource for learning.

This was great for helping me implement as programming function! I stumbled upon this video and It saved me so time and much pain!

This a very clear and simple explanation, Thank you so much !

This is THE best example I've seen on RU-vid. Thanks!

Thank you so much for this video I've been struggling like hell for the past three days trying to learn this!

Now I don't have to cram the example I have on my notes, I give you 100% for the tutorial 👏👏👏

You're amazing thank you so much for sharing this video and explaining concept in a way that finally makes sense to me!!!

Thanks a ton for this brilliant tutorial!

thank you so much for this absolutely BEAUTIFUL explanation.

This is very helpful. I have been struggling to solve this process chinese remainder theorem. You made it easier to learn.

Thanks! I audited a number theory course in college, but got too busy to do the homework, and absorbed very little as a result. Great refresher!

I wish I found your channel at the start of my semester, but better late than never! 💃🏾💃🏾💃🏾 You're a wonderful teacher.

Thanks, founding a good explenation of this topic was harder than way through The Misty Mountains in winter, you helped as much as eagles could help!

💯% Clear explanation.🇵🇭 Thanksss!

The extended euclidean algorithm really helps instead of trial or error for finding inverse.I have had some luck writing a computer program for it and now I wanted to understand the chinese remainder theorem and incorporate the the algorithm into it,but I was having a hard time until i came upon this video which blew my mind.Thank you so much,I have been stuck for days struggling with number theory and this helps so much.Please make more videos.

Thank you so much for making this video!

Thank you so much for the clear explanation. Your video really help me for a project in my crypto class.

Amazingly clear explaination!

This is really helpful. Very simple to understand. Thanks

Thank you, great and clear explanation! Cheers from Egypt! :)

you are just awsome lots of love 🥰such a patient.. delicate explanation i love it...

Poland here, thank you for this video. The best explained CRT on RU-vid

this video is extremly helpful. thanks alot!

Thank you! Your video helped me finish my assignment.

Thank you so much to recall my college maths in a very clear way.

thank you so much , this method is way easier than using the euclidean algorithm which gets quite confusing when finding the inverse

This video is the definition of life saving thanks alot !!

The best explaination ever. thanks alot.

"Beautiful, Beautiful, something close to genius." THANK YOU SO MUCH!!!!

The numbers are so small that I solved this problem in my head after a few minutes whilst watching the video. I just tried to find a values of x such that x = 6 + 8y, where y = 1,2,3, ... 9 (I stopped here) as 6 + 8x9 = 78, and x = 78 satisfied all three congruences.

Thank you so much for making this video :D

This really helps a lot. Thank you 😊

Thank you so much! This helped me a lot now :)

What a great explanation!!

Fantastic lucid explanation......

For finding the inverse, I personally find it easier to add ni to the right term until I get a multiple of the left term parameter. At least when the left term parameter is such that it is easy to check if a number divides it.

Thank you! That was really helpful

Thank you for making it easy for us to understand.

Wow simple and great explanation.

Amazing explained well done!

Thank you!! This was so simple

Thanks! Helped me with my final :D

thank you a lot! this video helped me out quite good and i hopefully will perform as good as i can at the midterm too..

You might be my hero of the day

Very helpful. Thanks!

thank you very much. this is so simple

Hello! You're one dedicated teacher, Jay.. this is one concept that looked unsurmountable, and you've helped me become competent in a matter of 13 minutes.. thank you so much.

Thank you so much for outstanding explanation

Even though I do have some tutorials in my native language which is Polish, this video was more helpful. Now I understand this and I'm ready for my exam

You are the best thanks so much!!!

I have a homework and I following your steps to solve it. Thank you so much ^^

Thanks for ur explanation

Thank you so much. I had headache understanding this

Thanks a lot for the explaination

Thanks!! Just learnt something I could not learn from fancy books.

gem of a video.

In India Artabhatta 1 invented in kuttaka ,ie pulverised system. He was born in 476 AD in India and possibly headed Belanda University.. See reminder theorem linear and Pell equation invented by brahma gupta in 628 AD. For all info see bbdatta ana ansingh book hindu mathematics. May be available in internet archive.

The math books I have are horrible at explaining it. They are all written by people who forget how hard this is to an outsider. This video was the best so far.

It's very simple.. Thanks a lot mam

You can explain really well

U r Genenious ✨🌟⚡✨ thanks a ton 🙌

Great explanation thanks

Excellent Explanation 🤗🤗🤗

Good Job...keep going love from Bangla

great explanation thanks!

wonderful video, crystal clear. i was able to implement Python code for this trivially, especially since Python 3.8 provides the function for the modular inverse with a simple call to `x = pow(Ni,-1,m)`, no libraries needed

Thank you for your time

Amazing explanation

Brilliant Jay! Thank you. Do you still do screencasts for OU?

Good explantion..Thank you..

Best tutorial!

Bro ur a life saver