Chapter: Quadratic Residues

This chapter is dedicated to quadratic residues. The concept has many applications we will learn about later, including cryptography and the factorization of large numbers.

  1. Definition: Quadratic Residue, Quadratic Nonresidue
  2. Definition: Legendre Symbol
  3. Proposition: Legendre Symbols of Equal Residues
  4. Proposition: Number of Quadratic Residues in Reduced Residue Systems Modulo a Prime
  5. Proposition: Euler's Criterion For Quadratic Residues
  6. Proposition: Multiplicativity of the Legendre Symbol
  7. Section: Calculating Legendre Symbols
  8. Section: Generalizations of the Legendre symbol - Jacobi and Kronecker Symbols

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  1. Landau, Edmund: "Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927