The multiplicative group modulo 17 is cyclic of order 16. The number of solutions to \( x^4 \equiv 1 \pmod17 \) is \( \gcd(4,16) = 4 \)? No — actually, the number of solutions to \( x^d \equiv 1 \pmodp \) is \( \gcd(d, p-1) \), so here \( \gcd(4,16) = 4 \). So there are 4 solutions. - Crosslake