MathDB

A sequence of the last digit of n^(n^n) is periodic

Source: Baltic Way 2006

December 4, 2010

modular arithmeticnumber theory proposednumber theory

Problem Statement

For a positive integer

n

let

a_n

denote the last digit of

n^{(n^n)}

. Prove that the sequence

(a_n)

is periodic and determine the length of the minimal period.