Number Theory | Linear Congruences Proposition 2

[@georgesadler7830]

Professor Penn, thank you for analyzing and explaining Linear Congruences in introductory Number Theory.

[@programstix3837]

This and next video out of order in this short playlist "Modular Arithmetic and Linear Congruences" FYI. Much appreciated videos!!

[@PunmasterSTP]

Congruence? More like con-fluence, of a bunch of amazing information! Thanks again so much for making and posting these videos!

[@adrilmanurung1730]

Thank you very much sir, I'm truly being helped by your videos

[@snipergranola6359]

How to solve linear congruence using Diophantine eq

[@ronycb7168]

Are they the only solutions to any linear congruence

[@ronycb7168]

ohk that's what distinct means right? got it after watching the whole video

[@prathikkannan3324]

Consider 2r = -3(mod 55), by the theorem there should be gcd(2,55) = 1 solution. But this is obviously false, why?

[@PunmasterSTP]

I think there is a solution. r = 26 is a solution, since 2(r) = 2(26) = 52 and -3 ≡ -3 + 55 ≡ 52 mod 55.

[@prathikkannan3324]

@@PunmasterSTP yes you are right, I was probably being stupid when I wrote that comment :)

[@PunmasterSTP]

@@prathikkannan3324 You're good; a lot of times I can get totally confused myself, especially with number theory!

[@thayanithirk1784]

R u working as a professor ??

[@MichaelPennMath]

Yes, I teach at Randolph College in central Virginia.

[@thayanithirk1784]

😊

[@paulkohl9267]

missed 12...

[@omiz8916]

i like it when he says good to himself lol

[@metehanturan8181]

x = 3 (mod 5) is the solution.

[@tonk6812]

U must first explain for the existence of the soln if d|b . If X°is a soln of ax=b(modn). Then n|aX°-b =>d.k|d.lX°-b =>d.k|d(l.X°-b/d) =>b/d€Z =>d|b