MathDB

(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}?

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