Question

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?

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Quadratic Residues

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