I'm sure someone wants to write out all the fun properties of Legendre symbols. It just happens not to be me right now. -- ComplexZeta

Is it any number n, or any integer n? --- cosinator

Where? --ComplexZeta 11:07, 27 June 2006 (EDT)

In the introduction it says 'We say that a is a quadratic residue modulo m if there is some number n so that n^2 − a is divisible by m.' If it were any number, I would think that any a could be a quadratic residue modulo m

Thanks for clarifying -Cosinator

Whereas the above are properties of the Legendre symbol, they still hold for any odd integers p and q when using the Jacobi symbol defined below. Hmmm... The quadratic reciprocity law clearly fails (at least in the form as written for primes) if $\gcd(m,n)>1$. So some correction is needed. My knowledge of number theory really needs some refreshment, so could someone else write the correct statement here? --Fedja 14:34, 28 June 2006 (EDT)

Yes, coprime was missing.

Rather than having this page link to a seperate page for the Legendre symbol, wouldn't it make more sense to just have the Legendre symbol page be a redirect here? (After all, there isn't anything to say about the L. symbol that doesn't say things about q. residues.)--JBL 10:01, 13 July 2006 (EDT)