MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
JHMT problems
2024 JHMT HS
7
Units Digit of Tetration
Units Digit of Tetration
Source:
September 8, 2024
number theory
2024
Problem Statement
Let
N
6
N_6
N
6
be the answer to problem 6. Given positive integers
n
n
n
and
a
a
a
, the
n
n
n
th tetration of
a
a
a
is defined as
n
a
=
a
a
⋅
⋅
⋅
a
⏟
n
times
.
^{n}a=\underbrace{a^{a^{\cdot^{\cdot^{\cdot^a}}}}}_{n \text{ times}}.
n
a
=
n
times
a
a
⋅
⋅
⋅
a
.
For example,
4
2
=
2
2
2
2
=
2
2
4
=
2
16
=
65536
^{4}2=2^{2^{2^2}}=2^{2^4}=2^{16}=65536
4
2
=
2
2
2
2
=
2
2
4
=
2
16
=
65536
. Compute the units digit of
2024
N
6
^{2024}N_6
2024
N
6
.
Back to Problems
View on AoPS