Definition talk:Legendre Symbol

I don't understand the section titled "applications". Surely the way this has been defined is precisely that:

$\left(\dfrac{a}{p}\right) = \begin{cases} 0 & : a \equiv 0 \pmod{p} \\ +1 & : a \mbox{ is a quadratic residue of } p \\ -1 & : a \mbox{ is a quadratic non-residue of } p \end{cases}$

from the definitions of Quadratic Residue and Quadratic Non-Residue?

I propose that the actual definition itself be worded in terms of QR and N-QR. Thoughts? --prime mover (talk) 20:35, 11 April 2009 (UTC)