18

Part of 2006 Baltic Way

Problems(1)

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

Source: Baltic Way 2006

For a positive integer

n

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.

modular arithmeticnumber theory proposednumber theory