1. Solve the following linear congruences.
(i) $3 x \equiv 2(\bmod 7)$;
(ii) $9 x \equiv 12(\bmod 15)$;
(iii) $7 x \equiv 1(\bmod 31)$;
(iv) $20 x \equiv 4(\bmod 30)$;
(v) $17 x \equiv 14(\bmod 21)$;
(vi) $64 x \equiv 83(\bmod 105)$;
(vii) $128 x \equiv 833(\bmod 1001)$;
(viii) $987 x \equiv 610(\bmod 1597)$;
(ix) $57 x \equiv 87(\bmod 105)$;
(x) $49 x \equiv 5000(\bmod 999)$.
1. (i) $x \equiv 3(\bmod 7)$;
(ii) $x \equiv 3,8,13(\bmod 15)$;
(iii) $x \equiv 9(\bmod 31)$;
(iv) $(20,30)=10 \nmid 4$, no solution;
(v) $x \equiv 7(\bmod 21)$;
(vi) $x \equiv 62(\bmod 105)$;
(vii) $1001=7 \cdot 11 \cdot 13 . x \equiv-189(\bmod 1001)$;
(viii) $x \equiv-1(\bmod 1597)$;
(ix) $x \equiv-4,31,66(\bmod 105)$;
(x) $x \equiv-163(\bmod 999)$.