1. Determine whether the following congruences are solvable. For those that are solvable, find all solutions:
(1) $x^{2} \equiv 43(\bmod 109)$.
(2) $x^{2} \equiv 247(\bmod 881)$.
(3) $x^{2} \equiv 7 \quad(\bmod 83)$.
(4) $x^{2} \equiv-11(\bmod 59)$.
(5) $x^{2} \equiv-5(\bmod 243)$.
(6) $x^{2} \equiv-46(\bmod 121)$.
(7) $x^{2} \equiv 41(\bmod 1024)$.
(8) $x^{2} \equiv 34(\bmod 495)$.
(9) $x^{2} \equiv 81(\bmod 729)$.
(10) $12 x^{2}-11 x-1 \equiv 0(\bmod 30)$.
(11) $x^{2}-10 x-11 \equiv 0(\bmod 90)$.