In the proof of the existence of a finite field with `p^2` elements for a prime p, we considered the polynomial `f(x) = x^2 - a in ZZ_p [x]`, where a is a specific element in `ZZ_p`. For p > 2, what crucial property must a possess for the construction of the field extension `ZZ_p[x]"/"langle x^2 - a rangle` to work:
A) a must be a quadratic residue modulo p.
B) a must be a quadratic non-residue modulo p ?