Number Theory

  1. Greatest Common Divisor and Least Common Multiple
    1. Greatest Common Divisor
      1. Definition and Notation
        1. Properties of GCD
          1. GCD and Prime Factorization
            1. Linear Combination Property
            2. Euclidean Algorithm
              1. Algorithm Description
                1. Step-by-Step Examples
                  1. Proof of Correctness
                    1. Efficiency and Complexity
                      1. Variants of the Algorithm
                      2. Extended Euclidean Algorithm
                        1. Algorithm Description
                          1. Bézout's Identity
                            1. Finding Linear Combinations
                              1. Applications to Modular Arithmetic
                              2. Least Common Multiple
                                1. Definition and Notation
                                  1. Properties of LCM
                                    1. LCM and Prime Factorization
                                      1. Relationship Between GCD and LCM
                                      2. Relatively Prime Integers
                                        1. Definition of Coprimality
                                          1. Properties of Relatively Prime Numbers
                                            1. Characterizations of Coprimality
                                              1. Applications in Number Theory

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                                            3. Prime Numbers and Factorization

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                                            5. Modular Arithmetic and Congruences