Question

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation
[a] · [x] = [b]
has (i) no solution,
(ii) exactly one solution for [x] ∈ Z6.
(b) Determine whether or not if it is possible to find [a] , [b] ∈ Z6 , so that the equation has
more than one solution.

Answer 1

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation[a] · [x] = [b]

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation[a] · [x] = [b]has (i) no solution,

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation[a] · [x] = [b]has (i) no solution,(ii) exactly one solution for [x] ∈ Z6.

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation[a] · [x] = [b]has (i) no solution,(ii) exactly one solution for [x] ∈ Z6. (b) Determine whether or not if it is possible to find [a] , [b] ∈ Z6 , so that the equation has

(a) Find [a] , [b] ∈ Z6, with [a] not equal to [0] so that the equation[a] · [x] = [b]has (i) no solution,(ii) exactly one solution for [x] ∈ Z6. (b) Determine whether or not if it is possible to find [a] , [b] ∈ Z6 , so that the equation hasmore than one solution.