Let ℤ17 be the ring of integers modulo 17, and let ℤ×17 be the group of units of ℤ17 under multiplication. which of the following are generators of ℤ×17? i.5 ii.8 iii.16
(i) 5.
(ii) 8.
(iii) 16.
(a) none.
(b) i only.
(c) ii only.
(d) iii only.
(e) i, ii, and iii

 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.

i dont know sorry

step-by-step explanation: