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Number Theory
Number Theory
43 lessons across 14 topics
1. Divisibility and Basic Proof
1
Divisibility Notation
2
Greatest Common Divisors
3
Linear Combinations
2. Euclidean Algorithm
4
Algorithm And Correctness
5
Applications To Solvability
6
Bézout’s Identity
3. Prime Numbers
7
Fundamental Theorem Of Arithmetic
8
Infinitude Of Primes
9
Prime Factorization Arguments
4. Congruences
10
Arithmetic Modulo N
11
Congruence Classes
12
Modular Arithmetic
5. Linear Congruences
13
Inverses Modulo N
14
Reduced Residue Systems
15
Solvability Conditions
6. Chinese Remainder Theorem
16
Applications
17
Constructive Solutions
18
Statement And Proof
7. Fermat and Euler
19
Euler’s Phi Function
20
Euler’s Theorem
21
Fermat’s Little Theorem
8. Midterm 1 and Arithmetic Functions
22
Divisor Sums
23
Midterm 1
24
Multiplicative Functions
25
Möbius Overview, If Included
9. Diophantine Equations I
26
Integer Solutions
27
Linear Diophantine Equations
28
Structural Reasoning
10. Diophantine Equations II
29
Pythagorean Triples
30
Selected Classical Problems
31
Sums Of Squares
11. Quadratic Residues Overview
32
Introductory Residue Theory If Included
33
Legendre Symbol Overview
34
Squares Modulo N
12. Continued Fractions or Cryptography Applications
35
Continued Fractions And Approximation
36
Key Themes In Continued Fractions Or Cryptography Applications
37
Or Modular Arithmetic In Rsa-style Systems
13. Advanced Topics (SLASH) Student Presentations
38
Independent Exploration Or Problem Sessions
39
Key Themes In Advanced Topics / Student Presentations
40
Selected Classical Theorems
14. Final Review
41
Applying Final Review
42
Key Themes In Final Review
43
Proof Synthesis And Structural Themes In Integer Arithmetic
