The letter 'n', underlined and written as a superscript. It's a way of shortening words on paper. Can't reproduce here, but Solution becomes Soln, Definition can be written Defn, Abbreviation as Abbrevn.
Hello, i dont know if you have the time but i've a question about Euler theorem. Let say you want to find phi(26), how do you do that ? without calculator. I dont understand how most teacher calculate phi so fast. (2-1)(13-1) = 12 We says that 2 divide 13 integers between 1 and 26, where does 13 come from ? I understand fermat little theorem but euler theorem..
I've find the answer somewhere, you have to divide 26 by 2 and once the rest is equal to 0 we divide the quotient by 2 redo til the rest is equal to 1. 26 = 2x13 + 0
The solution is 4 (mod 8), so anything of the form 4 + 8k will work. We originally wanted to solve in mod 32, so any value of k is fine as long as it yields a number between 0 and 31, so that's the final list of solutions: 4, 12, 20, 28.
Because our original goal was to solve a congruence modulo 32. I guess this isn't strictly necessary, but it is customary to exhibit your solution in terms of the original congruence.
@@MichaelPennMath thanks for replying me very fastly sir.I am from India and after going through lots of videos now i am able to understand the concept by you.may i know from which country and region you belong to?
I hated this as a student as well! It is so much more efficient to guess and check modular inverse for "small" n rather than go through the trouble of doing the Extended Euclidean Algorithm. Here is a video where I highlight the guess and check method along with the long method: ruclips.net/video/uPFh9_nLw1c/видео.html. Also, lots of research level mathematics is done via guess and check. The checking just involving writing a careful proof.
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THis man is the GOAT
Congruent? More like con-great! Thanks again for making all of these wonderful videos and uploading them to enlighten us.
Professor Penn, thank you for showing the Strategies for Solving Linear Congruence.
This finally makes sense now after watching this. Thank you!
How can we say that result in 3:22
Always interesting. Thanks for posting.
Hello your video is very easy to understand. I am confusing about what is the symbol you write after write “sol”?
The letter 'n', underlined and written as a superscript. It's a way of shortening words on paper. Can't reproduce here, but Solution becomes Soln, Definition can be written Defn, Abbreviation as Abbrevn.
nice, what a good video.
Hello, i dont know if you have the time but i've a question about Euler theorem.
Let say you want to find phi(26), how do you do that ? without calculator.
I dont understand how most teacher calculate phi so fast. (2-1)(13-1) = 12 We says that 2 divide 13 integers between 1 and 26, where does 13 come from ?
I understand fermat little theorem but euler theorem..
I've find the answer somewhere, you have to divide 26 by 2 and once the rest is equal to 0 we divide the quotient by 2 redo til the rest is equal to 1.
26 = 2x13 + 0
I still dont get it i can't calculate phi(72) !!!
Alright i found the solution, we have to split 72 in primes 72 = 2^3*3^2 then phi(72)=72(1-1/2)(1-1/3)=24 easy clap ^^
why are the solutions mod 32 instead of mod 8 like the previous step?
The solution is 4 (mod 8), so anything of the form 4 + 8k will work.
We originally wanted to solve in mod 32, so any value of k is fine as long as it yields a number between 0 and 31, so that's the final list of solutions: 4, 12, 20, 28.
Amazing
Why did you got back to mod(32)?
Because our original goal was to solve a congruence modulo 32. I guess this isn't strictly necessary, but it is customary to exhibit your solution in terms of the original congruence.
Sorry sir,but i understood partially.actually i got stuck at how you take 12 mod 8 and then divide it to 4 mod 8.please guide us.
12 is 4 larger than 8 so the remainder after dividing is 4, therefore 4 mod 8.
-Stephanie
MP Editor
@@MichaelPennMath thanks for replying me very fastly sir.I am from India and after going through lots of videos now i am able to understand the concept by you.may i know from which country and region you belong to?
i hate when they do a trial-and-error guess for the multiplicate inverse. i see it in every modulo video and it's stupid.
I hated this as a student as well! It is so much more efficient to guess and check modular inverse for "small" n rather than go through the trouble of doing the Extended Euclidean Algorithm. Here is a video where I highlight the guess and check method along with the long method: ruclips.net/video/uPFh9_nLw1c/видео.html.
Also, lots of research level mathematics is done via guess and check. The checking just involving writing a careful proof.
Bro this is one of THE WORST math tutorials ever, going over concepts too fast, bare explanation, it's like a recap video rather than a tutorial.