Quadratic Reciprocity Law

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External reading guide · Undergraduate

Quadratic reciprocity relates whether one odd prime is a square modulo another to the reversed question. The Legendre symbol and Gauss's lemma turn the sign rule into a method for reducing computations.

Before opening the references

Integer Congruence · Fermat's Little Theorem

Where to read

  1. Start here: Quadratic Residues, Quadratic Reciprocity, Lecture 9 Notes

    Abhinav Kumar (course instructor; MIT OpenCourseWare) · Lecture notes · English · Free full text

    Lecture 9, Legendre Symbol, Lemma 40 (Gauss Lemma), and Theorem 42 (Quadratic Reciprocity Law)

    Source page · Checked 2026-10-16

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Elementary Number Theory in the library · Preparation and skip guidance

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