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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

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)

[1272] Landau, Edmund: “Vorlesungen ├╝ber Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927