Problem 3. (a) Formulate the necessary and sufficient condition for an integer a to have an inverse modulo n (where n > 2). (b) Use the Extended Euclid Algorithm to find the inverse of 12 modulo 77. (c) Find all solutions of 10x + 9 = 3 (mod 22) or prove that none exists. (d) Find all solutions of 10x +3 = 11 (mod 30) or prove that none exists