I have a problem in a textbook that is giving me trouble. Either I'm missing something or there is some sort of mistake in the question. The problem is with part (ii), the other parts seem okay, but I'll post all parts anyway:

Let be a prime number, and let be the group of integers , with multiplication modulo .

(i) Show that if then and deduce that .

(ii) Show that if then and decude that

(iii) Use parts (i) and (ii) to show that the order of the element 2 in is

(iv) Decude that is a power of 2.