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Factorial: n!|a^n+1

Source: IMO Shortlist 2005 N4, Iran preparation exam

April 24, 2006
factorialmodular arithmeticnumber theoryDivisibilityexponentialIMO ShortlistChinese Remainder Theorem

Problem Statement

Find all positive integers n n such that there exists a unique integer a a such that 0≤a<n! 0\leq a < n! with the following property: n!\mid a^n \plus{} 1
Proposed by Carlos Caicedo, Colombia
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