IMO Shortlist 1993 problem N1


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2. travnja 2012.
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A natural number n is said to have the property P, if, for all a, n^2 divides a^n - 1 whenever n divides a^n - 1.

a.) Show that every prime number n has property P.

b.) Show that there are infinitely many composite numbers n that possess property P.
Izvor: Međunarodna matematička olimpijada, shortlist 1993