Question: It is straightforward to solve, for x, any equation of the form
x +n a = b
in Zn, and to see that the result will be a unique value of x. On the other hand, we saw that 0, 3, 6, and 9 are all solutions to the equation
4 ·12 x = 0.
(a) Are there any integral values of a and b, with 1 ≤ a, b 12 x = b does not have any solutions in Z12? If there are, give one set of values for a and b. If there are not, explain how you know this.
(b) Are there any integers a, with 1 12 x = b has a solution? If so, give one and explain why it works. If not, explain how you know this.