Only \( n \equiv 1 \pmod{8} \) satisfies \( n^3 \equiv 1 \mod 8 \)? Try \( n = 9 \): \( 9^3 = 729 \equiv 1 \mod 8 \)? \( 729 \div 8 = 91 \times 8 = 728 \), so \( 729 \equiv 1 \). Yes.