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Show that every prime number n has property P

Source: IMO Shortlist 1993, India 5

March 15, 2006
modular arithmeticnumber theoryDivisibilityprime numberscomposite numbersIMO Shortlist

Problem Statement

A natural number nn is said to have the property P,P, if, for all a,n2a, n^2 divides an−1a^n - 1 whenever nn divides an−1.a^n - 1. a.) Show that every prime number nn has property P.P. b.) Show that there are infinitely many composite numbers nn that possess property P.P.
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