## 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

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[1272] **Landau, Edmund**: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

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