Uploaded September 2020 | Updated September 2026, 2 weeks ago
Fermat's little theorem gives us a general result about raising numbers to a power in modular arithmetic. But can we get more specific? That's where orders come in! We also prove that the order is multiplicative under certain conditions.
Quadratic Residues playlist: youtube.com/playlist?list=PLug5ZIRrShJGJieICD2KnqU9cRioaEBjB
0:00 Definition and Example
1:36 Multiples of the order of x
6:14 Order is multiplicative
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Music: OcularNebula - The Lopez
Fermat's little theorem gives us a general result about raising numbers to a power in modular arithmetic. But can we get more specific? That's where orders come in! We also prove that the order is multiplicative under certain conditions.
Quadratic Residues playlist: youtube.com/playlist?list=PLug5ZIRrShJGJieICD2KnqU9cRioaEBjB
0:00 Definition and Example
1:36 Multiples of the order of x
6:14 Order is multiplicative
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez
![I Want to Play a Game: Proving [0,1] is Uncountable](https://i.ytimg.com/vi/Mcfnnp8rxkI/mqdefault.jpg "I Want to Play a Game: Proving [0,1] is Uncountable
The interval [0,1] is uncountable, and there are many ways to prove that. Cantors diagonal argument is a classic example. But theres another way: proof by playing a game. This video is an explanation of a proof by contradiction after assuming that the infinite set [0,1] is countable and playing a game on that interval. All we need is basic calculus for the limits of sequences!
Original based on Grossman & Turett: https://arxiv.org/pdf/math/0606253
Calculus Problems playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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Music: C418 - Smooth Fall")
