17. Solve the congruence equations using methods that both utilize and do not utilize primitive roots:
(i) $x^{4} \equiv 41(\bmod 37) ;$
(ii) $x^{4} \equiv 37(\bmod 41)$.
17. (i) i.e., $\left(x^{2}-2\right)\left(x^{2}+2\right) \equiv 0(\bmod 37),\left(\frac{-2}{37}\right)=\left(\frac{2}{37}\right)=-1$, no solution;
(ii) $x \equiv 10,33,31,8(\bmod 41)$.