IMO Shortlist 1969 problem 23


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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}?
Izvor: Međunarodna matematička olimpijada, shortlist 1969