International Mathematical Olympiad 1991 Problem 2

Let $n > 6$ be an integer and $a_1, a_2, \ldots, a_k$ be all the natural numbers less than $n$ and relatively prime to $n$. If

$$a_2 - a_1 = a_3 - a_2 = \cdots = a_k - a_{k-1} > 0,$$

prove that $n$ must be either a prime number or a power of 2.