In this episode, I'll show you some clock-like number tricks that reveal patterns about exponents, prime numbers, "pseudoprimes", other bases, and more! See below for timestamps of different parts (and related episodes I've made)
0:00 - Introduction
0:24 - An Interesting Trait About Last Digits
2:47 - Connecting the Mathematics to Clocks
6:09 - Why 0, 1, 5, and 6 Did a Special Thing
9:30 - Interesting Symmetries Within Our Base
11:15 - Prime Mods/Bases and Fermat's Little Theorem
16:01 - Pseudoprimes and Carmichael Numbers
19:27 - A Further Generalization / A Chaotic Outro
Here are some previous episodes I've made related to modular arithmetic: (which can be watched either before or after this video)
About modular multiplication: https://youtu.be/hH89nUGd6DU?si=d0vqjcJfexWO3bCk
About modular division: https://youtu.be/Qh_SjdWnKpc?si=cJDZaMfSjYj0zcox
About "Wilson's theorem": https://youtu.be/jx2qGlNwiP4?si=zi4TAhrDDxJfj1za
(And many of my other episodes are also related to modular arithmetic in more subtle ways!)
Make sure you're also subscribed to my @Domotro channel for bonus content!
Special thanks to all of my supporters on Patreon! (Supporting the show not only helps me keep improving my content, but also lets me avoid having any product placements from brands in episodes)
Evan Clark, Max, George Carozzi, Peter Offut, Tybie Fitzhugh, Henry Spencer, Mitch Harding, YbabFlow, Joseph Rissler, Plenty W, Quinn Moyer, Julius 420, Philip Rogers, Ilmori Fajt, Brandon, August Taub, Ira Sanborn, Matthew Chudleigh, Cornelis Van Der Bent, Craig Butz, Mark S, Thorbjorn M H, Mathias Ermatinger, Edward Clarke, and Christopher Masto, Joshua S, Joost Doesberg, Adam, Chris Reisenbichler, Stan Seibert, Izeck, Beugul, OmegaRogue, Florian, William Hawkes, Michael Friemann, Claudio Fanelli, The Green Way, Julian Zassenhaus, Bailey Douglass, Jan Bosenberg, Brooks Boutwell, David Irvine, qe, George Sharabidze, Jack Dwyer, Fredrik, and Dave Brondsema!
If you want to help support this channel (and get your name on that list) and get some bonus content, check out the Patreon here: https://www.patreon.com/comboclass
If you want to mail me anything (such as any clocks/dice/etc. that you'd like to see in the background of Grade -2), here's my private mailbox address (not my home address). If you want to, please watch this short video first: https://youtu.be/_-gSvbvO8W4
Domotro
1442 A Walnut Street, Box # 401
Berkeley, CA 94709
Combo Class Discord server: https://discord.gg/cHHvDcPPuc
Subreddit: https://www.reddit.com/r/comboClass
If you want to try to help with Combo Class in some way, or collaborate in some form, reach out at combouniversity(at)gmail(dot)com
In case anybody searches any of these terms to learn about them, some topics in this video include: exponents, modular arithmetic, modular multiplication, modular exponentiation, base ten and other numeral bases like base two (binary) and various others, mathematics related to clocks, prime numbers, pseudoprime numbers such as Fermat pseudoprimes, Carmichael numbers, Fermat's Little Theorem, Euler's (Totient) Theorem, and more!
This episode was directed/edited/soundtracked by me (Domotro) and was filmed by Carlo Trappenberg.
Disclaimer: Do NOT copy any dangerous-seeming actions you may see in this video, such as any actions related to fire.