Number Theory

  1. Arithmetic Functions
    1. Introduction to Arithmetic Functions
      1. Definition and Examples
        1. Additive Functions
          1. Multiplicative Functions
            1. Completely Multiplicative Functions
            2. The Divisor Function
              1. Definition of τ(n)
                1. Properties and Formulas
                  1. Computing τ(n)
                    1. Average Order of τ(n)
                    2. Sum of Divisors Function
                      1. Definition of σ(n)
                        1. Properties and Formulas
                          1. Computing σ(n)
                            1. Variants of σ(n)
                            2. Möbius Function
                              1. Definition of μ(n)
                                1. Properties of μ(n)
                                  1. Möbius Inversion Formula
                                    1. Statement and Proof
                                    2. Connection to Other Functions
                                    3. Perfect Numbers
                                      1. Definition and Examples
                                        1. Even Perfect Numbers
                                          1. Euclid-Euler Theorem
                                            1. Connection to Mersenne Primes
                                            2. Odd Perfect Numbers
                                              1. Existence Question
                                                1. Known Properties
                                              2. Other Important Functions
                                                1. Liouville Function
                                                  1. Jordan's Totient Function
                                                    1. Ramanujan's τ Function

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                                                  6. Classical Theorems in Number Theory

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                                                  8. Diophantine Equations