Automorphic Numbers

Описание: We just passed 90,625 subscribers here, so let me explain about how that's the only 5-digit "automorphic" number in base ten (and then discuss/show some other stuff)... Timestamps of particular topics:
0:00 - intro
1:08 - 90000 vs 90625
1:52 - looking beyond base-dependent traits
3:15 - main topic (explaining automorphic numbers) starts here
3:32 - which 1-digit numbers keep their last digit when raised to powers?
5:48 - moving up to "automorphic" numbers with multiple digits
8:00 - lists of the two main families of automorphic numbers in base ten
10:40 - automorphic numbers in other bases
12:58 - my cat Dandelion visits
13:55 - back to automorphic numbers in different bases
15:34 - transitioning to answering questions from chat
15:56 - answering a question about square roots of primes
17:40 - continued fractions of square roots
20:24 - about the fake "Combo Class Bonus 2" channels
22:42 - some Combo Class plans for February
25:26 - my favorite number base(s)
30:13 - more about the Bonus channels my viewers are making
32:34 - number like 11 ("b+1") getting special abilities in bases
37:03 - looking through some of wikipedia's lists of numbers
44:27 - answering a question about "Harshad numbers"
46:04 - some last cat-petting and random chatting

Also check out my new bonus video about why February has 8! minutes here:    • Why This February Has Exactly 8! Minutes  

Combo Class links:
Patreon:   / comboclass  
Main channel:    / comboclass  
Subreddit:   / comboclass  
Discord:   / discord  

Combo Class, taught by Domotro, is a crazy educational show where you can have fun learning rare things about math, science, language, and more! This is the channel for Combo Class SHORTS and EXTRAS - make sure you're also subscribed to the main Combo Class channel where full episodes go!

DISCLAIMER: any use of fire, tools, or other science experiments in this series is always done in a safe and professional way. Do not try to copy any actions you see in this series yourself.