Fermat's Little Theorem ← Number Theory

Fermat's Little Theorem was observed by Fermat and proven by Euler, who generalized the theorem significantly. This theorem aids in dividing extremely large numbers and can aid in testing numbers to see if they are prime. For more advanced students, this theorem can be easily proven using basic group theory.

Prerequisites: To follow this video, you will want to first learn the basics of congruences.

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Subject: Number Theory
Teacher: Michael Harrison
Artist: Katrina de Dios

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[ansonngpersonalgoogleaccou]

The simplest and easiest-to-understand proof I have ever seen. Thank you!!!

[Fjgreeny]

Wow, thank you!! You've saved me. I now understand Fermat's little theorem for solving a^very large power. Your second example (3^100, 000) was excellently explained.

[samhenri]

Best explanation of this theorem I've seen on Youtube, thank you.

[Darieee]

I'm not sure if you're not just showing off your keyboard shortcut prowess in this video ._.

[Hintical]

That proof was so nice, huge thanks to you :)

[seymayumurta]

l have exam tomorrow and now i am finally fine with this part.. Thank you so much for your help i am so glad 🙏🙏

[DUBhoptillidrop]

Great and clear explanation of the proof! Thank you

[mathbyfaith]

You explained this so clearly and calmly, thank you!

[prashantjha]

best available video on Euler theorem
keep it up

[amethystklintberg]

I love this! I’ve seen similar proofs of Fermat’s Little Theorem before, but this explanation really clicked!

[AngeofDrkness]

Thanks for the video. I was like "this theorem is so easy", but wasn't sure how to apply it. Hopefully this helps with my Applied Cryptography final (well studying for)

[rulofmg]

"not elementary enough." - Richard Feynman.

[thrunsalmighty]

Very nicely done.
So much better than by those who scribble on bits of paper

[PunmasterSTP]

Fermat's Little Theorem? More like "Fear not! It's a little theorem, " after watching this Socratica video! Thanks for explaining this in such a great way!

[srijangupta]

Beautiful proof presented in a beautiful manner !

[RakhaKanzKautsar]

well, you can test some random number into the theorem
a^(p-1)=1(mod p)
for your case (458), you can try random a, like 2:
is 2^(458-1)%p=1?
if it yes, then your case *probably* is a prime, to make sure, you can test for another 'a' value.

[TopAhmed]

could anybody explain to me at 4:17 how he did the simplification to get 28 ?? please

[richardurena]

Great video! Wish my professor would stop and use visual aids for his lectures.

[Super_Shaq]

Great video! Could you expand on Number Theory at all?? Currently trying to grasp the concept of the Euler Totient Function and the RSA Method D:

[BoonkiCoC]

Holy, this little theorem is powerful as hell