Proof of Fermat's Little Theorem

Jesus Christ is NOT white. Jesus Christ CANNOT be white, it is a matter of biblical evidence. Jesus said don't image worship. Beyond this, images of white Jesus are not just blasphemous and criminal, white Jesus is from Satan ( the imposter.) Why? Let's look at what Satan does:
1) He is incredibly narcissistic and promotes himself shamelessly.
2) He misleads and confuses.
3) He pushes people away from Jesus Christ God, the Holy Trinity, the one and only messiah. White Jesus does all three of the above and more -- matching the ways of Satan.

Statues of Christ are equally offensive to God the Christ. While money is the biggest idol, Jesus spoke sufficiently against carved images.
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You can also find me on Tik Tok @reuslovesmath and @polarpiny

In the rearrangement piece, I moved by analogy instead of rigorous proof. The rigor missing is cumbersome not hard and would make this less accessible to some.
Math videos by Subject ( Proof of Fermat's Little Theorem is in Number Theory):

[IDK_OR_DO_I]

7:22 okay I'll keep watching...jk jk great vd btw!

[Ptoad]

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.

[lgooch]

I’ve been studying for competitive math and when I want to know why something is, you’re always there. Nice explanations

[LedCepelin]

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!

[chamaeelegans]

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.

[VersatileAnthem]

how can you say p does not divide (p-1)! .lets see for 8 . 7!/8 = 630. if i am wrong please clarify.

[hassanalabdullah]

hhhh. felt like if you were a friend explaining to me. keep it up

[ayshakhan]

Thanks for teaching this in such a short time🤗 ....otherwise i could not understand even in 40 mints😏

[demogorgon]

Gonna love your videos more after seeing this.. It's really cool that you explain these stuff in so less time. ✌

[alyaeminaga]

Thank you so much, this is literally the only understandable proof all over the internet

[chunlangong]

a could be bigger than p. for instance 7^2 congruent to 1 (mod 3) where gcd(7, 3)=1

[lexinaut]

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).

[zzzyout]

5:10, why is the products equal to each other?

[skauddy]

The proof was quite intuitive..
Thanks..🔥🔥

[collinskariuki]

In the last step, i don't get why it is a^(p-1)*(p-1)! instead of a*(p-1)! please explain.