"ALGEBRA QUESTION OF THE DAY'

If p divided by 9 leaves a remainder of 1, which of the following must be true?
I. p is even.
II. p is odd.
III. p = 3 ⋅ z + 1 for some integer z.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only