Respuesta :
Answer: The correct option is (E) I, II and III.
Step-by-step explanation: Given that ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication.
We are to select the correct generators of ℤ×17.
According to the given information, we can write
ℤ17 = {0, 1, 2, 3, . . . , 16}
and
ℤ×17 = {1, 2 , 3 , . . . 16}.
The generators of ℤ×17 are those elements which are co prime to 17.
Since all the elements from 1 to 16 are co prime to 17, so all the elements of the set ℤ×17 are its generators.
Therefore, 5, 8 and 16, all are generators. So, i, ii and iii are generators.
Thus, (E) is the correct option.
