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!
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
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.
@@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.
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?
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)
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.
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
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!
So glad you found it clear, thanks a lot! Looking forward to making more lessons on the topic!
I wish i found this before my exams! Absolutely golden explanation
Thanks for this clear explanation of how it works for negative numbers. I finally understand it now.
Thank you!! The example right in the beginning helped a lot.
Good morning sir
Excellent explanation
I am from Tamil Nadu
Thank you sir
Thanks for clean explanation
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?
Thank you SO much
Best explaination, Thank you sir
Thank you!
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
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
thank you, very useful and it helps alot . .
Thank you for watching, I am glad it helped! Let me know if you ever have any lesson requests!
Good job.
Thank you, Ron!
bless got my final in 2 weeks
Good luck! Thanks for watching and let me know if you have any questions!
Good explanation. Thank u sir.
Glad it helped! You're welcome and thanks a lot for watching!
Thank you so much sir. Very helpful😇
Glad to hear it! Thanks for watching, Rochelle!
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.
thank you for the video, sir.
how about this?
Find x:
1. 8 = x (mod 3)
2. x = 38 (mod 4)
I think x might be equal to 38
@@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.
@@fergusjohnson3788 ooo yes
Very useful
Glad to hear it, thanks for watching!
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?
how to get 2 remainder after dividing 2 by 4
Helpful ❤️
Glad to hear it, thanks for watching!
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?
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)
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)
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.
Thank you so much! Big help
I want to know about thereom on this topic
Thanks for watching, Murali! Is there a particular theorem you have in mind you'd like to see?
1:40 how you get 0 on 4=0.6+4
wiping my tears....still trying to get it
Do you have any questions I can help clear up?
Nice
Thanks for watching!
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
I'm glad to help! Thanks for watching and let me know if you have any questions!