4

Part of 2009 Chile National Olympiad

Problems(1)

x + 1, x^x + 1, x^{x^x}+1,... are divisible by 2009

Source: Chile Finals 2009 L2 p4

Find a positive integer

x

x> 1

such that all numbers in the sequence

x + 1,x^x + 1,x^{x^x}+1,...

are divisible by

2009.

dividesdivisiblenumber theory