3. Use Theorem 2 to determine:
(i) whether -8 is a quadratic residue modulo 53;
(ii) whether 8 is a quadratic residue modulo 67.
3. (i) $(-8)^{26} \equiv 11^{13} \equiv 11 \cdot 15^{6} \equiv 11 \cdot 13^{3} \equiv -16 \cdot 10 \equiv -1(\bmod 53), -8$ is not a quadratic residue modulo 53; (ii) $8^{33} \equiv 8 \cdot (3)^{16} \equiv 8 \cdot 14^{4} \equiv 8 \cdot 5^{2} \equiv -1(\bmod 67), 8$ is not a quadratic residue modulo 67.