![(FRA 6)](/media/m/6/c/4/6c41ca035126add62a3339c21d177196.png)
Consider the integer
![d = \frac{a^b-1}{c}](/media/m/c/c/0/cc0e683770d7c8ce5e8fad4b65eb8bfa.png)
, where
![a, b](/media/m/a/2/b/a2bdbf048e2daac0a021a1d79f6fb9bf.png)
, and
![c](/media/m/e/a/3/ea344283b6fa26e4a02989dd1fb52a51.png)
are positive integers and
![c \le a.](/media/m/1/8/e/18eb3b560d764681735a368908880106.png)
Prove that the set
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
of integers that are between
![1](/media/m/a/9/1/a913f49384c0227c8ea296a725bfc987.png)
and
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
and relatively prime to
![d](/media/m/f/7/d/f7d3dcc684965febe6006946a72e0cd3.png)
(the number of such integers is denoted by
![\phi(d)](/media/m/5/c/5/5c57794154cb2ac441c197ac55b6cdfa.png)
) can be partitioned into
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
subsets, each of which consists of
![b](/media/m/e/e/c/eec0d7323095a1f2101fc1a74d069df6.png)
elements. What can be said about the rational number
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$(FRA 6)$ Consider the integer $d = \frac{a^b-1}{c}$, where $a, b$, and $c$ are positive integers and $c \le a.$ Prove that the set $G$ of integers that are between $1$ and $d$ and relatively prime to $d$ (the number of such integers is denoted by $\phi(d)$) can be partitioned into $n$ subsets, each of which consists of $b$ elements. What can be said about the rational number $\frac{\phi(d)}{b}?$