You may not need this information now; however, if you are still confused : Here is an easy way of finding the inverse ☺: Below we mod 1 through 5 by adding 19 each step: 1→ 2 → 3 → 4 → 5 1 ≡ 20 ≡ 39 ≡ 58 ≡ 77 Then we take the result from the 5th computation and divide it by the modulo (19) Which gives us the multiplicative inverse solution of 4 (or quotient): 77 ÷ 19 = 4 ← [this is the quotient] • 19 + 1 Therefore; 5^-1 ≡ 4 (mod 19) Meaning that: 4 • 19 = 76 [with a remainder of 1, which is the gcd] Thus, giving us: 4 • 19 + 1 = 77
The symbol with four lines at 0:20, Are you trying to symbolize congruence? I couldn't find this symbol in wikipedia en.wikipedia.org/wiki/Modular_arithmetic#Congruence_relation
While this method is simple and easy to understand, when it comes to slightly larger numbers, I feel like one would still have to resort to the extended Euclidean algorithm. e.g. find inverse of 23 mod 59: 23 ≡ -36 (mod 59) …
5 = -2 mod 7. The answer is both, because 5 and -2 are the same number in this case. Really what's going on is when we write 5, we mean the set {...,-9,-2,5,12,...} and that set is called the equivalence class. Modular arithmetic is arithmetic on equivalence classes. For example, (using modulo 7), 5+2 really means {...,-9,-2,5,12,...} + {...,-12,-5,2,9,...} = {...,-14,-7,0,7,...}. You are adding or multiplying sets, but it's not obvious how to multiply a set with a set. It turns out you can just pick any number from a set to represent it, and do the usual arithmetic with that number. So, adding the equivalence classes of 5 and 2, we have 5+2 = 12+9 = -7 = 0 = 7 for example. It doesn't matter what representative you pick.
You may not need this information now; however, if you are still confused : Here is an easy way of finding the inverse: Below we mod 1 through 5 by adding 19 each step: 1→ 2 → 3 → 4 → 5 1 ≡ 20 ≡ 39 ≡ 58 ≡ 77 Then we take the result from the 5th computation and divide it by the modulo (19) Which gives us the multiplicative inverse solution of 4 (or quotient): 77 ÷ 19 = 4 ← [this is the quotient] • 19 + 1 Therefore; 5^-1 ≡ 4 (mod 19) Meaning that: 4 • 19 = 76 [with a remainder of 1, which is the gcd] Thus, giving us: 4 • 19 + 1 = 77
Thank you again. You truly explain the concept of multiplicative inverse.
You are amazing for this video. Completely changed how I solve these problems and makes it so much simpler than the Extended Euclidean Algrotihmn
my words, this is an awesome teacher
I still didn't understand it.
you will never do xD
You may not need this information now; however, if you are still confused :
Here is an easy way of finding the inverse ☺:
Below we mod 1 through 5 by adding 19 each step:
1→ 2 → 3 → 4 → 5
1 ≡ 20 ≡ 39 ≡ 58 ≡ 77
Then we take the result from the 5th computation and divide it by the modulo
(19)
Which gives us the multiplicative inverse solution of 4 (or quotient):
77 ÷ 19 = 4 ← [this is the quotient] • 19 + 1
Therefore; 5^-1 ≡ 4 (mod 19)
Meaning that:
4 • 19 = 76 [with a remainder of 1, which is the gcd]
Thus, giving us:
4 • 19 + 1 = 77
@@joeynavarro4528 i am anable to understand mam
@@joeynavarro4528 I don't think that this works for other modulos.Take any of her examples and you won't find the modulo.
Thanks! Would be even better if you had an example of large numbers e.g., 3761 = 1 mod 31363
thank you very much, this tutorial exactly made me understand finding inverse!
great video. you made this very simple to understand. Thanks.
It finally clicked for me after watching this video, thank you so much
You’re welcome 😊
The symbol with four lines at 0:20, Are you trying to symbolize congruence?
I couldn't find this symbol in wikipedia en.wikipedia.org/wiki/Modular_arithmetic#Congruence_relation
Thanks a lot for excellent and understandable lecture!! I spent several hours on google, but I could not get clear idea. Thanks a lot again.
Thank you so muchh missssssssssssssssssssssssss
you are the goat for this
what is the name of this technique?
what is the name of this algorithm ??
Can you please provide its reference ?
While this method is simple and easy to understand, when it comes to slightly larger numbers, I feel like one would still have to resort to the extended Euclidean algorithm.
e.g. find inverse of 23 mod 59:
23 ≡ -36 (mod 59)
…
Thank you so much for this mam. It really got me the clarity and these tricks are really important for everyone, exams are not easy🥲
I love you and your videos sooo much.................Thank you for uploading them.
Thank you soo much for this video!! Helped immensely
I hope you have more videos.
Thank you so much, it cleared all of my doubts.
Excellent.
Great Video but i have a question. 5^-1 /// 3 mod 7 , i have found 15 /// 1 mod 7
I would like to know if the same result
Perfect explanation thank you👍 please make more videos like this👍❤️💓
Please, let me know the inverse of 3 modulo 7 ???
Is it 5 or -2?
I am confused and how to solve?
5 = -2 mod 7. The answer is both, because 5 and -2 are the same number in this case.
Really what's going on is when we write 5, we mean the set {...,-9,-2,5,12,...} and that set is called the equivalence class. Modular arithmetic is arithmetic on equivalence classes. For example, (using modulo 7), 5+2 really means {...,-9,-2,5,12,...} + {...,-12,-5,2,9,...} = {...,-14,-7,0,7,...}. You are adding or multiplying sets, but it's not obvious how to multiply a set with a set. It turns out you can just pick any number from a set to represent it, and do the usual arithmetic with that number. So, adding the equivalence classes of 5 and 2, we have 5+2 = 12+9 = -7 = 0 = 7 for example. It doesn't matter what representative you pick.
i get it but i still don't get how it working out translates to answer
That's very clear thank you cathy
How about if I'm looking for inverses under addition of modulo? is this technique can be applied?
Thanks, very helpful
you are welcome, glad it helped!
Excellent
Thank you, very easy to understand.
omggg thank you!!! you did way better than my college professor at explaining this
Amazing trick
What if it 3x=2[5] what can i do
what if you have larger numbers
Perfect ❤🎉🎉
saved my life
Thankyou mam maja aa gaya
Thank you very much
thanks a lot.
very efficient
very gooddd thankss alott
THANK YOU!!
Thank you!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
thank u.
What?!
mmm not understanding
You may not need this information now; however, if you are still confused :
Here is an easy way of finding the inverse:
Below we mod 1 through 5 by adding 19 each step:
1→ 2 → 3 → 4 → 5
1 ≡ 20 ≡ 39 ≡ 58 ≡ 77
Then we take the result from the 5th computation and divide it by the modulo
(19)
Which gives us the multiplicative inverse solution of 4 (or quotient):
77 ÷ 19 = 4 ← [this is the quotient] • 19 + 1
Therefore; 5^-1 ≡ 4 (mod 19)
Meaning that:
4 • 19 = 76 [with a remainder of 1, which is the gcd]
Thus, giving us:
4 • 19 + 1 = 77
😮
Просто спасибо
🤍
really BAD explination
Bro what this is good