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.

- Definition: Quadratic Residue, Quadratic Nonresidue
- Definition: Legendre Symbol
- Proposition: Legendre Symbols of Equal Residues
- Proposition: Number of Quadratic Residues in Reduced Residue Systems Modulo a Prime
- Proposition: Euler's Criterion For Quadratic Residues
- Proposition: Multiplicativity of the Legendre Symbol
- Section: Calculating Legendre Symbols
- Section: Generalizations of the Legendre symbol - Jacobi and Kronecker Symbols

**Landau, Edmund**: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927