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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.

Table of Contents

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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References

Bibliography

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