Number Theory

Notes on number theory from A Classical Introduction to Modern Number Theory by K. Ireland and M. Rosen.

Note: Numbering on lemmas and corollaries do not match the numbering as it appears in the book.

Contents§

• 1
  Unique Factorization
• 2
  Applications of Unique Factorization
• 3
  Congruence
• 4
  The Structure of $U(\mathbb{Z}/n\mathbb{Z})$
• 5
  Quadratic Reciprocity
• 6
  Quadratic Gauss Sums
• 7
  Finite Fields
• 8
  Gauss and Jacobi Sums
• 9
  Cubic and Biquadratic Reciprocity
• 10
  Equations over Finite Fields
• 11
  Zeta Function
• 12
  Algebraic Number Theory