Theory Problems Solve the following problems. 1. Show whether or not the set of remainders Z12 forms a group with either one of the modulo addition or modulo multiplication operations. 2. Compute ged(29495, 16983) using Euclid's algorithm. Show all the steps. 3. With the help of Bezout's identity, show that if c is a common divisor of two integers a, b > 0, then cged(a,b) (i.e. c is a divisor of ged(a,b)). 4. Use the Extended Euclid's Algorithm to compute by hand the multiplicative inverse of 25 in Z. List all of the steps. 5. In the following, find the smallest possible integer x. Briefly explain (i.e. you don't need to list out all of the steps) how you found the answer to each. You should solve them without using brute-force methods: (a) 8x = 11 (mod 13) (b) 5x = 3 (mod 21) (c) 8x = 9 (mod 7)