Number Theory | Inverses modulo n

[@ronycb7168]

Your channel is one of the most top go-to channels when it comes to college math, and I'm here 5 years after this playlist was made. Helping me a great deal lot...

[@thinguyen8865]

Thanks you teacher Penn for dedicating time and energy to create awesome math videos that helps simplify math like this. It helps students around the world who struggle with math a lot.

[@azharlatif6228]

Michael Penn is Super human embodying as Mathematician, Mountaineer, Diver and what not. Saw his Q n A footage to know him. Stay Blessed Michael !!!

[@macerdough]

You deserve the world for this.

[@azizketata3241]

the tyoe of teacher who will fuckk you up if you're not attentive . Keep lifting man.

[@gorgzilla1712]

Thank you so much for being so clear and concise in all these videos; really helps a lot! Subscribed.

[@ramakrishnasen4386]

Try taking off your earphones and watching this video! The magic is, you'll still understand what he wants to explain!!

[@ryanl3184]

Yeah... Speakers are just bigger versions of earphones.

[@Nothingtonnobodson]

@@ryanl3184 lol

[@georgesadler7830]

Professor Penn, thank you for fantastic analysis on Inverses modulo n. These are classic topics in Number Theory.

[@Walczyk]

michael penn is doing the world a great service, really for anyone interested in pure math

[@MyOneFiftiethOfADollar]

Noticed for arbitrary modulus n that (n-1)(n-1)==(-1)(-1)=1 (mod n) Put another way, n-1 is it’s own inverse (mod n). Also consistent with n and n-1 being relatively prime. Special case of this is what you showed (8)(8)==1 (mod 9)

[@kakalibiswas1312]

Thanks sir for giving free knowledge of number theory

[@zianwang2897]

Great work! Keep it up.

[@PunmasterSTP]

I know that you just discussed inverses, but I have to say that this video was singular. Thanks again for making all of these!

[@hypnovia]

If you can have the inverse of a number mod n… what’s stopping there from being an inverse of a MATRIX mod n? What if det(M) mod n is equal to 0, or not relatively prime to n?

[@she_wizzdom4410]

Finally understood it ! Thanks

[@Ensivion]

so for only prime n, do each of the non-zero minimal residues have an actual 'modulo inverse', and n-1 always is its own inverse, I have a feeling this is very important when studying primes.

[@TJStellmach]

Yes, in fact this criterion means that any ring of integers modulo a prime number is also a field, and therefore a host of theorems which hold in fields are available.

[@ren5124]

How do we prove that these inverse pairs are unique?

[@chrisjuravich3398]

So influenced am I by these videos that I find myself saying “good“ after each time I make a true statement of fact.

[@sonusdulcis]

Thank you Mr. Penn 🙏🙏🙏

[@tiandao1chouqin]

Nice work. At 7:32, about the reverse direction proof, you said you proved it in the channel before, could you provide the link? Thanks!

[@Orion6479]

Can students follow lessons being taught this fast?

[@williamjones3731]

Great videos

[@MichaelPennMath]

Thanks!

[@sgssergio]

Hi teacher, in 1:56 you write 2^-1 = 5 mod 9 , 5^-1 cong 2 mod 9. In the first why do you use equal sumbol and not congruence symbol instead?

[@dominickmancine6033]

It's just a "typo". The multiplicative inverse of any number that's congruent to 2 (mod 9) is any number that's congruent to 5 (mod 9). But to avoid using all of those words people usually just say the inverse of 2 (mod 9) *is* 5. That implies equality, but congruence is really just a "loose" equality. I think whenever you say (mod n) you really should use the congruence symbol, but sometimes people forget. Also, in the comments on his videos people will use the = symbol because it's not obvious how to type the congruence symbol.

[@Tytyshippy]

GOOD.

[@GauravKumar-bk7hh]

mast

[@2on1masti9]

Thank you sir

[@kobethebeefinmathworld953]

I'll say it's more like a ring theory problem

[@abdelrhmanahmed1378]

because its a ring theory problem !:)

[@kArnAgePT]

good

[@ToanPham-wr7xe]

😮

[@jonatanorange6491]

Great content, but Bruh, in the future recordings please stop missing steps and call them "tricks".

[@mgd891]

hot