IMO Shortlist 1991 problem 15


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Let \,n > 6\, be an integer and \,a_{1},a_{2},\cdots ,a_{k}\, be all the natural numbers less than n and relatively prime to n. If
a_{2} - a_{1} = a_{3} - a_{2} = \cdots = a_{k} - a_{k - 1} > 0,
prove that \,n\, must be either a prime number or a power of \,2.
Izvor: Međunarodna matematička olimpijada, shortlist 1991