Example 2 Use Theorem 2 to determine:
(i) whether 3 is a quadratic residue modulo 17;
(ii) whether 7 is a quadratic residue modulo 29.
From $3^{3} \equiv 10(\bmod 17), 3^{4} \equiv 30 \equiv-4(\bmod 17), 3^{8} \equiv-1(\bmod 17)$ we know that 3 is a quadratic non-residue modulo 17.

From $7^{2} \equiv-9(\bmod 29), 7^{3} \equiv-5(\bmod 29), 7^{6} \equiv-4(\bmod 29), 7^{7} \equiv$ $1(\bmod 29), 7^{14} \equiv 1(\bmod 29)$ we know that 7 is a quadratic residue modulo 29.