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.

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 !!!

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

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

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

Great work! Keep it up.

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

@ryanl3184

3 жыл бұрын

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

@Nothingtonnobodson

3 жыл бұрын

@@ryanl3184 lol

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

Thanks sir for giving free knowledge of number theory

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)

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

Finally understood it ! Thanks

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!

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?

Thank you Mr. Penn 🙏🙏🙏

GOOD.

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

3 жыл бұрын

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.

How do we prove that these inverse pairs are unique?

Thank you sir

Great videos

@MichaelPennMath

4 жыл бұрын

Thanks!

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

mast

good

😮

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

@abdelrhmanahmed1378

3 жыл бұрын

because its a ring theory problem !:)

6:32 Could anyone explain this step for me?!

@mysto5107

Жыл бұрын

it's a theorem that any linear combination of 2 numbers a and b, has to be a multiple of the gcd. since the only divisor of 1 is 1, then the gcd has to be 1.

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

3 жыл бұрын

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.

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

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