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

Source: Chile Finals 2009 L2 p4

October 5, 2022
dividesdivisiblenumber theory

Problem Statement

Find a positive integer xx, with x>1x> 1 such that all numbers in the sequence x+1,xx+1,xxx+1,...x + 1,x^x + 1,x^{x^x}+1,... are divisible by 2009.2009.
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