Number Theory

  1. Classical Theorems in Number Theory
    1. Fermat's Little Theorem
      1. Statement of the Theorem
        1. Multiple Proofs
          1. Combinatorial Proof
            1. Group Theory Proof
              1. Induction Proof
              2. Applications and Examples
                1. Generalizations
                2. Wilson's Theorem
                  1. Statement of the Theorem
                    1. Proof of Wilson's Theorem
                      1. Converse of Wilson's Theorem
                        1. Applications in Primality Testing
                        2. Euler's Totient Function
                          1. Definition and Notation
                            1. Basic Properties
                              1. Computing φ(n)
                                1. For Prime Powers
                                  1. For General n
                                  2. Multiplicativity
                                    1. Statement and Proof
                                    2. Sum and Product Formulas
                                    3. Euler's Theorem
                                      1. Statement of the Theorem
                                        1. Proof Using Group Theory
                                          1. Relationship to Fermat's Little Theorem
                                            1. Applications in Cryptography

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                                          5. Modular Arithmetic and Congruences

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                                          7. Arithmetic Functions