5.1 Number Theory
Explore the powers of divisibility, modular arithmetic, and infinity.
Last Digits
Secret Messages
Rainbow Cycles
Divisibility Shortcuts
More Divisibility Shortcuts
Divisibility by 9 and 3
Last Digits
Arithmetic with Remainders
Digital Roots
Factor Trees
Prime Factorization
Factoring Factorials
Counting Divisors
100 Doors
How Many Prime Numbers Are There?
100 Doors Revisited
The LCM
Billiard Tables
The GCD
Dots on the Diagonal
Number Jumping (I)
Number Jumping (II)
Number Jumping (III)
Relating LCM and GCD
Billiard Tables Revisited (I)
Billiard Tables Revisited (II)
Times and Dates
Modular Congruence
Modular Arithmetic
Divisibility by 11
Star Drawing (I)
Star Drawing (II)
Star Drawing (III)
Die-Hard Decanting (I)
Die-Hard Decanting (II)
Additive Cycles
Modular Multiplicative Inverses
Multiplicative Cycles
Fermat's Little Theorem
Totients
Last Digits Revisited
Perfect Shuffling
Counting to Infinity
Multiple Infinities
Hilbert's Hotel
Infinitely Large
The Invention of Number Bases
Introducing Binary
Binary on Computers
Exploding Dots
Binary
Binary Operations
Perfect Shuffles
Hexadecimal
Hexadecimal Operations
An Unusual Computer Base
Divisibility
Last Digits Rules
More Divisibility Rules
Cryptograms Solved by Divisibility
Cryptogram Addition Puzzles
Cryptogram Variety Pack
Factorial Refresher
Calculation Tricks
Digital Roots
Terminating Decimals
Repeating Decimals
Repeating Patterns
Problem Solving
Hexadecimal Divisibility Shortcuts (I)
Hexadecimal Divisibility Shortcuts (II)
Hexadecimal Divisibility Shortcuts (III)
Divisibility Shortcuts in Other Bases
Hexadecimal Last Digits
Last Digits in Other Bases
Course description
This course starts at the very beginning — covering all of the essential tools and concepts in number theory, and then applying them to computational art, cryptography (code-breaking), challenging logic puzzles, understanding infinity, and more!
Topics covered
- Divisibility Shortcuts
- Exploring Infinity
- Factor Trees
- Fermat's Little Theorem
- Greatest Common Divisor
- Least Common Multiple
- Modular Arithmetic
- Modular Congruence
- Modular Inverses
- Prime Factorization
- The 100 Doors Puzzle
- Totients
Prerequisites and next steps
A basic understanding of exponents and multiplication is all you need!