Let
be an integer and
be all the natural numbers less than
and relatively prime to
. If
prove that
must be either a prime number or a power of
.
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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 $\,2$.
Školjka