Euler's Totient Theorem and Fermat's Little Theorem - Complete Proof & Intuition

thank you

That was absolutely insane, my text book really had a field day with making it extremely complicated by using maps.

This was clear and I was able to see the magic, I was blown away by the result of this proof

Thank you so so much

thanks so much ! just a small question : is saying that a isn't multiple of p, the same as gcd(a,p) = 1 ?

bro really made me think fr, amazing video

Thank you! Is the best proof of this theorem I've seen!

So straightforward! Good Lecturer

your really good at speaking

Very neat. Amazing work. Thank you!

Would I get a higher mark in my meth test if I wrap my head with a towel?

Oh wow, I knew about Fermat's little theorem but I had no idea it was a special case of this one. Cool video, but I might need to get slightly more comfortable with some of the fundamentals of modular arithmetic to completely get the rules, though you seem to have videos for that too, which helps.

Great Video. The concept seemed so abstract without seeing the intuition behind it. Now it makes total sense!

What if a is a negative integer

I'm merely struggling with this and can't even understand a thing. Thank you sooo much for keeping everything straight

Thank you! A very good proof

Very clear explanation! Great!!!

You sound a bit like Addison Anderson who narrates the tedX videos!

I am curious here as to why you are putting out videos on so many varied math topics? Is this a project? Anyway good luck going to Caltech. If I can ask you, what for you is the most interesting work going on right now. In science or math or other?

Jesus christ man I started looking into modular arithmetic without knowing anything about it beforehand as part of a high school assignment, and your clear explanations helped me understand everything in such a way, that even 5-10 other videos couldn't accomplish! Keep up the good work, you deserve so many more views and subs!

I can understand this with secondary school math, meaning a great job done by you. Thanks

The injection part... if we define f(x) = ax mod n, and gcd(a,n) = 1 , then if x1 =/= x2 , f(x1) =/= f(x2)

You're great!! Keep making more videos :D

Thank you so much it really helped

Best, most clear, concise least stuttery explanation I've ever seen of the Proofs of the Totient Theorem. Also amazing proof of FLT. Congrats!!

Amazing video. Clear and detailed explanations.

Excellent video! thank you

Love you Sir. You are helping people

This is a pretty neat proof of these theorems!
It's simple, straightforward, and not at all tedious, good job!
Do you plan on doing a video on the Chinese remainder theorem?

The best demonstration I ever saw about this ! Thank you

Which college have you choose?

nice video i was looking for a neat proof of the totient formula for a while now and you did it!