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This question concerns the quadratic residues in the additive group ZN .(An element y ∈ ZN is a quadratic residue if and only if there exists an x ∈ ZN with 2x = y mod N.)
(a) Let p be an odd prime. How many elements of Zp are quadratic residues?
(b) Let N = pq be a product of two odd primes p and q. How many elements of ZN are quadratic residues?
(c) Let N be an even integer. How many elements of ZN are quadratic residues?
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How are they the same? How are they different?
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