Number Theory

  1. Quadratic Residues and Reciprocity
    1. Quadratic Residues
      1. Definition and Basic Properties
        1. Quadratic Non-residues
          1. Examples and Computations
          2. Legendre Symbol
            1. Definition and Notation
              1. Basic Properties
                1. Computational Rules
                  1. Multiplicativity
                  2. Euler's Criterion
                    1. Statement and Proof
                      1. Connection to Fermat's Little Theorem
                      2. Gauss's Lemma
                        1. Statement and Proof
                          1. Applications to Quadratic Reciprocity
                          2. Quadratic Reciprocity Law
                            1. Main Reciprocity Law
                              1. First Supplement
                                1. Quadratic Character of -1
                                2. Second Supplement
                                  1. Quadratic Character of 2
                                  2. Proof Strategies
                                    1. Applications and Examples
                                    2. Jacobi Symbol
                                      1. Definition and Properties
                                        1. Relationship to Legendre Symbol
                                          1. Computational Advantages

                                        Previous

                                        8. Diophantine Equations

                                        Go to top

                                        Next

                                        10. Prime Number Theory