Let
![\,n > 6\,](/media/m/7/8/f/78fd88c4fe67e79d8badab64173ae3ef.png)
be an integer and
![\,a_{1},a_{2},\cdots ,a_{k}\,](/media/m/9/9/6/9969150cb80a8015ca4f5ffff9500803.png)
be all the natural numbers less than
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
and relatively prime to
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
. If
prove that
![\,n\,](/media/m/3/2/e/32e4ed37300f0cd666553950dba3bcad.png)
must be either a prime number or a power of
![\,2](/media/m/8/1/e/81ef64cb83dc892e63580b42a26019b6.png)
.
%V0
Let $\,n > 6\,$ be an integer and $\,a_{1},a_{2},\cdots ,a_{k}\,$ 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 $\,2$.