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Quadratic Residues

Is there a perfect square that leaves a remainder of 7 when divided by 82? We don't need to list out all the squares, but just need to check that (7/82)=-1.

Quadratic Residues - Primes


Is 5 a quadratic residue modulo 7?

Which of these is the set of non-quadratic residues modulo \(11\)?

Which of these is the set of quadratic residues modulo \(15\)?

Find the sum of all positive integers \(x<22 \) such that \(x^2 \equiv 17 \pmod {22} \).

Is \(15\) a quadratic residue modulo \(17\)?


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