1. Solve the following congruences using the index table:
(i) $3 x^{6} \equiv 5(\bmod 7)$;
(ii) $x^{12} \equiv 16(\bmod 17)$;
(iii) $5 x^{11} \equiv-6(\bmod 17)$;
(iv) $3 x^{14} \equiv 2(\bmod 23)$;
(v) $x^{15} \equiv 14(\bmod 41)$;
(vi) $7 x^{7} \equiv 11(\bmod 41)$;
(vii) $3^{x} \equiv 2(\bmod 23)$;
(viii) $13^{x} \equiv 5(\bmod 23)$.
1. (i) no solution;
(ii) $x \equiv 1,13,16,4(\bmod 17)$;
(iii) $x \equiv 2(\bmod 17)$;
(iv) $x \equiv-9(\bmod 23)$;
(v) $x \equiv 29,3,30,13,7(\bmod 41)$;
(vi) $x \equiv 4(\bmod 41)$;
(vii) $x \equiv 7,18(\bmod 22)$;
(viii) no solution.