Theory of numbers: Quadratic reciprocity

Описание к видео Theory of numbers: Quadratic reciprocity

This lecture is part of an online undergraduate course on the theory of numbers.

We state and law of quadratic reciprocity for Legendre symbols, and prove it using Gauss sums. As applications we show how to use it to calculate Legendre symbols and to test Fermat numbers to see if they are primes.

Update: As pointed out in a comment, the estimate of the number of proofs of the quadratic reciprocity law in the lecture is out of date. The book "The Quadratic Reciprocity Law" by Oswald Baumgart lists 314 proofs as of 2014.

For the other lectures in the course see    • Theory of numbers  

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