Quadratic residues of Z ∗.

We can also consider the quadratic residues of the additive group Zn (i.e. any element y ∈ Zn is a quadratic residue if and only if there exists an x ∈ Zn with 2x = y mod n.).

(a) What are the quadratic residues in Zp for p an odd prime?

(b) Let n = pq be a product of two odd primes p and q. What are the quadratic residues in Zn ?

(c) Let n be an even integer. What are the quadratic residues in Zn?

**Subject Mathematics Advanced Math**