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.

| | | | created: 2019-05-12 08:44:46 | modified: 2019-05-12 08:46:07 | by: bookofproofs | references: [1272]

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.Calculating Legendre Symbols 

8.Generalizations of the Legendre symbol - Jacobi and Kronecker Symbols