This lecture is part of an online undergraduate course on the theory of numbers.
We describe Gauss's lemma which gives a useful criterion for whether a number n is a quadratic residue of a prime p. We work it out explicitly for n = -1, 2 and 3, and as an application prove some cases of Dirichlet's theorem. Finally we use it to show that the Legendre symbol (n/p) for fixed n depends only on p mod 4n.
For the other lectures in the course see • Theory of numbers
Негізгі бет Theory of numbers: Gauss's lemma
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