This law conjectured by Leonhard Euler (1707 – 1783) and first proven by Carl Friedrich Gauss (1777 - 1855).
Theorem: Quadratic Reciprocity Law
Let and be odd and distinct prime numbers. Then the product of the Legendre symbols has the following explicit formula:
In particular:
* If then the congruences and are either both solvable or both not solvable.
* If then one of the congruences and is solvable, the other not solvable.
Table of Contents
Proofs: 1
Mentioned in:
Proofs: 1 2
Solutions: 3
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References
Bibliography
- Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927