Well, it is pretty easy to guess from the answer what happens. You are asked for "the product of all positive integers less than n such that ..." and find that the product is 1. The only way a product of integers can equal 1 is if all the integers are 1! It must be the case that the only positive integer, x, such that "every integer from 1 to p-1 can be written as a power of x in modulo p" is 1 itself.