What is Modular Congruence? | Congruence Modulo n, Modular Congruence Definitions

[@mandy7212]

This is the most clear and concise intro to mods I have found on YT. I will definitely be sharing this with my students. Keep up the great instructional content!

[@WrathofMath]

So glad you found it clear, thanks a lot! Looking forward to making more lessons on the topic!

[@maxien101]

I wish i found this before my exams! Absolutely golden explanation

[@shambo9807]

Thanks for this clear explanation of how it works for negative numbers. I finally understand it now.

[@nancynguyen2244]

Thank you!! The example right in the beginning helped a lot.

[@daisyg509]

Thank you SO much

[@rajendranchockalingam1079]

Good morning sir Excellent explanation I am from Tamil Nadu Thank you sir

[@luisdfernandez2601]

I have to laugh. I kept asking myself "how did he get 4 as a remainder??" And then, I remembered we're dealing with whole numbers and that 6 can't go into 4 therefore it is 0 and the remainder is the actual 4. It had me scratching my temple for a minute or two LOL

[@madihachaklader2378]

I thought it’s only me… as for a moment I thought it’s 0.6 then I realised it’s 0 multiplied with 6 hahah

[@srinidhinagendran7523]

Thanks for clean explanation

[@luisdfernandez2601]

On 3:50 do you mean a = 14 and b = 8? Because on the previous example you used the same numbers as an example but got a positive 2 as a remainder and here you get a -2 as remainder.

[@yousufh5053]

thank you, very useful and it helps alot . .

[@WrathofMath]

Thank you for watching, I am glad it helped! Let me know if you ever have any lesson requests!

[@janabaijadhav7490]

Best explaination, Thank you sir

[@WrathofMath]

Thank you!

[@RonUS2009]

Good job.

[@WrathofMath]

Thank you, Ron!

[@rochellealonzo8519]

Thank you so much sir. Very helpful😇

[@WrathofMath]

Glad to hear it! Thanks for watching, Rochelle!

[@saritha9623]

Good explanation. Thank u sir.

[@WrathofMath]

Glad it helped! You're welcome and thanks a lot for watching!

[@jairoselin5119]

Helpful ❤️

[@WrathofMath]

Glad to hear it, thanks for watching!

[@johnw1368]

Thank you! Could you please do a video on solving congruence equation? Ex , ax= b (mod") etc etc. But could you please break it down very easily?

[@mm-wm6uh]

1:40 how you get 0 on 4=0.6+4

[@universalponcho]

Very useful

[@WrathofMath]

Glad to hear it, thanks for watching!

[@oshawastaken]

bless got my final in 2 weeks

[@WrathofMath]

Good luck! Thanks for watching and let me know if you have any questions!

[@AbuBakar-f4n6d]

how to get 2 remainder after dividing 2 by 4

[@srinidhinagendran7523]

I want to know about thereom on this topic

[@WrathofMath]

Thanks for watching, Murali! Is there a particular theorem you have in mind you'd like to see?

[@user-is8fw2je1y]

Hi, I have doubt. There are 2 ways of solving modulo systems I guess. So my professor gave an example: 14 congruent 2 (mod 12). We solved it like: 14-2=12, and 12 would be an integral multiple of m. But when I tried the same problem with your method, I am getting different remainders for both. Why is that?

[@mandy7212]

14 = 1(12) + 2 2 = 0(12) + 2 I read this mentally as: "14 is 1 multiple of 12 plus 2", and "2 is 0 multiples of 12 plus 2". In both cases, the remainder is 2. Thus, 14 ≡ 2 (mod 12). Note it is the case that 12 | (14-2) or 12 | (2-14)

[@julventuba1515]

Can you give example of this theorem? if ca and cb is congruent mod n, then a and b congruent modulo n/d where d= gcd (c,n)

[@WrathofMath]

Thanks for watching! Sure, let c = 12, a = 3, and b = 7. Then ca = 36 and cb = 84. Then we have a few options for n if we want congruence mod n. Let's pick n = 8. Notice 36 is congruent to 84 mod 8. Then, d = gcd(12, 8) = 4. Thus, the theorem tells us 3 is congruent to 7 mod 8/4. Simplifying we have 3 is congruent to 7 mod 2. Indeed this is true, as 7 - 3 is divisible by 2, or equivalently, they both have remainder 1 when divided by 2.

[@julventuba1515]

Thank you so much! Big help

[@ahmedmghabat7982]

3/n(n^2 -1) ? For every n natural Actually i had it in my previous exam to answer if its true or false . Please can you solve it?

[@exercisefitnesshealth8965]

thank you for the video, sir. how about this? Find x: 1. 8 = x (mod 3) 2. x = 38 (mod 4)

[@OMPRAKASHVerma-dh6ve]

I think x might be equal to 38

[@fergusjohnson3788]

@@OMPRAKASHVerma-dh6ve when we divide 8 by modulus 3 (8:3), then we obviously get the result with a remainder 2. So, to get 8 back, we have to multiply 2 by 3 and finally add 2 (8=2*3+2). To get X, we use the same division strategy when it comes to dividing x by 3 (x:3). As b=x, a=8, and c=3, we have to find the number as when it is divided by 3 the remainder should exactly be 2. So, it is 38. PROOF: 38=12*3+2.

[@OMPRAKASHVerma-dh6ve]

@@fergusjohnson3788 ooo yes

[@jamaicarabino7897]

Nice

[@WrathofMath]

Thanks for watching!

[@d12kiem7]

wiping my tears....still trying to get it

[@WrathofMath]

Do you have any questions I can help clear up?

[@koshka02]

My prof is so garbage compared to these videos My prof doesn't explain anything, and I'm genuinely trying my hardest to learn then I go here and you explain it so simply My tuition should be going here, not my prof

[@WrathofMath]

I'm glad to help! Thanks for watching and let me know if you have any questions!