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Chile Contests
Chile National Olympiad
2021 Chile National Olympiad
1
1
Part of
2021 Chile National Olympiad
Problems
(1)
last digit of a_{2021} if a_n = 7^{a_{n-1}}
Source: 2021 Chile National Olympiad level 2 p1
10/22/2022
Consider the sequence of numbers defined by
a
1
=
7
a_1 = 7
a
1
=
7
,
a
2
=
7
7
a_2 = 7^7
a
2
=
7
7
,
.
.
.
...
...
,
a
n
=
7
a
n
−
1
a_n = 7^{a_{n-1}}
a
n
=
7
a
n
−
1
for
n
≥
2
n \ge 2
n
≥
2
. Determine the last digit of the decimal representation of
a
2021
a_{2021}
a
2021
.
number theory
Last digit
recurrence relation