Number Theory | Strategies for Solving Linear Congruence

[@MarcusSt0ne]

This finally makes sense now after watching this. Thank you!

[@PunmasterSTP]

Congruent? More like con-great! Thanks again for making all of these wonderful videos and uploading them to enlighten us.

[@georgesadler7830]

Professor Penn, thank you for showing the Strategies for Solving Linear Congruence.

[@kevinzurita9907]

THis man is the GOAT

[@muneerahammed4114]

How can we say that result in 3:22

[@IODell]

Always interesting. Thanks for posting.

[@MetalNeo91]

nice, what a good video.

[@MetalNeo91]

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..

[@MetalNeo91]

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

[@MetalNeo91]

I still dont get it i can't calculate phi(72) !!!

[@MetalNeo91]

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 ^^

[@yongnianguan4273]

Hello your video is very easy to understand. I am confusing about what is the symbol you write after write “sol”?

[@paulconnor1040]

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.

[@vika0u0]

why are the solutions mod 32 instead of mod 8 like the previous step?

[@TheOiseau]

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.

[@snipergranola6359]

Amazing

[@anantshelgaonkar3950]

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.

[@MichaelPennMath]

12 is 4 larger than 8 so the remainder after dividing is 4, therefore 4 mod 8. -Stephanie MP Editor

[@anantshelgaonkar3950]

@@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?

[@dwightd3659]

Why did you got back to mod(32)?

[@MichaelPennMath]

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.

[@hazzard77]

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.

[@MichaelPennMath]

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: kzbin.info/www/bejne/q4GpmWyVo7GqZ8U. Also, lots of research level mathematics is done via guess and check. The checking just involving writing a careful proof.

[@evanthechong2167]

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.