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last digit of a_{2021} if a_n = 7^{a_{n-1}}

Source: 2021 Chile National Olympiad level 2 p1

October 22, 2022

number theoryLast digitrecurrence relation

Problem Statement

Consider the sequence of numbers defined by

a_1 = 7

a_2 = 7^7

...

a_n = 7^{a_{n-1}}

for

n \ge 2

. Determine the last digit of the decimal representation of

a_{2021}