Definition: Quadratic Residue, Quadratic Nonresidue

Let $m > 0$ be a positive integer. An integer $n\in\mathbb Z$ is called a quadratic residue modulo $m,$ if the congruence $$x^2(m)\equiv n(m)$$ is solvable, otherwise it is called a quadratic nonresidue.

Examples

Definitions: 1
Explanations: 2
Problems: 3
Proofs: 4 5 6
Propositions: 7 8 9


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References

Bibliography

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