I was so stuck with this one, and was looping around Euclids division lemma as a vehicle of the proof(which are the classes I suppose). This makes much more sense to me, thank you!
I could follow the proof up until you said a(1, 2, 3, ..., p-1) ≡ 1, 2, 3, ..., p-1 (mod p) Why is this necessarily the case? I realized you justified it by showing the example of a = 8 with the modulus being p = 5, but that's hardly an exhaustive proof.
I think I got it. If sa ≡ ta (mod p), then because gcd(a, p) = 1, we have s ≡ t (mod p), so the multiples a, 2a, 3a, ..., (p-1)a (mod p) must necessarily be distinct.
I mean thats pretty much common sense and if your are looking at fermats little theorem it should be assumed as trivial, but as a proof, assume that a>p-1? If a = p then a = 0 if a is greater than p we can say a =m*p + k for some natural m and natural k
THANKS! This is by far the clearest and most helpful proof of this theorem for a more general audience I have seen. I was not a math major (I'm simply fascinated by the splendors of mathematics).
I’ve been studying for competitive math and when I want to know why something is, you’re always there. Nice explanations
I was so stuck with this one, and was looping around Euclids division lemma as a vehicle of the proof(which are the classes I suppose). This makes much more sense to me, thank you!
You're very welcome JB. It is cool that you spend a lot of time to understand math, that is the best way to learn!
Thank you so much, this is literally the only understandable proof all over the internet
I could follow the proof up until you said
a(1, 2, 3, ..., p-1) ≡ 1, 2, 3, ..., p-1 (mod p)
Why is this necessarily the case? I realized you justified it by showing the example of a = 8 with the modulus being p = 5, but that's hardly an exhaustive proof.
I think I got it.
If sa ≡ ta (mod p), then because gcd(a, p) = 1, we have s ≡ t (mod p), so the multiples a, 2a, 3a, ..., (p-1)a (mod p) must necessarily be distinct.
kjQtte thank you sir
I mean thats pretty much common sense and if your are looking at fermats little theorem it should be assumed as trivial, but as a proof, assume that a>p-1? If a = p then a = 0 if a is greater than p we can say a =m*p + k for some natural m and natural k
how can you say p does not divide (p-1)! .lets see for 8 . 7!/8 = 630. if i am wrong please clarify.
I will answer later cause I have to watch the video to answer your question.
@@ChristGodinyouItrust i got it the reason is p is always a prime
@@VersatileAnthem Yeah cool bud:)
Gonna love your videos more after seeing this.. It's really cool that you explain these stuff in so less time. ✌
Thanks a lot Rabin, I appreciate the encouraging messages:) Hope you had a great day!
THANKS! This is by far the clearest and most helpful proof of this theorem for a more general audience I have seen. I was not a math major (I'm simply fascinated by the splendors of mathematics).
great work !! hope you get more views
Thank you my dude, found this in spam for some reason!
Nice explanation
Amazing bro
Thank you man, glad you like:)
Thank you for the lesson
Cheers!
Really helpful thank you 😊
hhhh. felt like if you were a friend explaining to me. keep it up
I like your comment. And I like the hhh.
Awesome ❤❤❤
Great explanation, thank you!
Your channel is good.
Thank you subscribe and let your friends know about it.
@@ChristGodinyouItrust I have already subscribed 😊.
@@architmahatorollno.332 Thank you!
5:10, why is the products equal to each other?
Thanks for teaching this in such a short time🤗 ....otherwise i could not understand even in 40 mints😏
Glad to hear Aysha! Thank you for wanting to learn:)
The proof was quite intuitive..
Thanks..🔥🔥
Cheers Sandeep.
7:22 okay I'll keep watching...jk jk great vd btw!
Really helpful, thanks!!!
Cheers Javier.
I liked your jolly mood
Thank you boss!
Thanks man!
You're very welcome!
In the last step, i don't get why it is a^(p-1)*(p-1)! instead of a*(p-1)! please explain.
Because you have a*2a*...*(p-1)a= a multiplied by itself (p-1) times and also 1*2*...(p-1) so that makes a^(p-1)*(p-1)!
nice video! where are u from?
Knowledge, Knowledge, New York but I want to go back to my country so bad. I am from Ethiopia so I am an alien.
Why this rearrange ment works?
Some number theory idea, I think I mention it, I don't remember, sorry!
This is a nice explanation, but not really a proof. You have shown an example, which was good :). Just that you have not proven anything.
I agree! Great observation!
Why is it not a proof?
@@LedCepelin Because it is a bit incomplete in parts and pieces.
a could be bigger than p. for instance 7^2 congruent to 1 (mod 3) where gcd(7,3)=1
great proof🙏👍
Cheers Soroush!
Not even a proof.
❤❤❤
First