10

Part of 2006 Switzerland - Final Round

Problems(1)

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

Source: Switzerland - 2006 Swiss MO Final Round p10

Decide whether there is an integer

n > 1

with the following properties: (a)

n

is not a prime number. (b) For all integers

a

a^n - a

is divisible by

n

number theorydivisibledivides