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1 1 The Principle of Mathematical Induction
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Number Theory
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- 1 0 Introduction
- 2 1 1 The Principle of Mathematical Induction
- 3 1 2 The Basis Representation Theorem
- 4 2 1 The Division Algorithm
- 5 2 2a Divisibility
- 6 2 2b The Euclidean Algorithm
- 7 2 3 Linear Diophantine Equations
- 8 2 4 The Fundamental Theorem of Arithmetic
- 9 3 1 Permutations and Combinations
- 10 3 2 Fermat's Little Theorem
- 11 3 3 Wilson's Theorem
- 12 3 5 Computer Programming
- 13 4 1 Basic Properties of Congruences
- 14 4 2 Residue Systems
- 15 5 1 Linear Congruences
- 16 5 2 Fermat's Little Theorem and Wilson's Theorem
- 17 5 3 The Chinese Remainder Theorem
- 18 6 1a The Euler Phi Function Part 1
- 19 6 1b The Euler Phi Function Part 2
- 20 6 2 6 3 Multiplicative Functions
- 21 6 4 The Mobius Inversion Formula
- 22 7 1 Orders of Elements
- 23 7 2 Primitive Roots Modulo p
- 24 8 1 The Prime Counting Function
- 25 9 1 Euler's Criterion
- 26 9 2 The Legendre Symbol
- 27 9 3a Quadratic Reciprocity Part 1
- 28 9 3b Quadratic Reciprocity Part 2
- 29 9 4 Applications of Quadratic Reciprocity
- 30 10 1 Consecutive Residues
- 31 10 2a Consecutive Triples of Residues Part 1
- 32 10 2b Consecutive Triples of Residues Part 2
- 33 11 1 Sums of Two Squares
- 34 11 2 Sums of Four Squares
- 35 15 1 Gauss' Circle Problem
- 36 15 2 Dirichlet's Divisor Problem
- 37 Infinity Conclusion
