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a^n-a is divisible by n , for all integers a

Source: Switzerland - 2006 Swiss MO Final Round p10

December 26, 2022
number theorydivisibledivides

Problem Statement

Decide whether there is an integer n>1n > 1 with the following properties: (a) nn is not a prime number. (b) For all integers aa, anāˆ’aa^n - a is divisible by nn