Consider the integer
, where
, and
are positive integers and
Prove that the set
of integers that are between
and
and relatively prime to
(the number of such integers is denoted by
) can be partitioned into
subsets, each of which consists of
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 $\frac{\phi(d)}{b}?$
Školjka