Question 23
(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 $\varphi(d)$) can be partitioned into $n$ subsets, each of which consists of $b$ elements. What can be said about the rational number $\frac{\varphi(d)}{b}$?