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2010 VTRMC
Problem 2
75^75^75^ (2^100 times) mod 17
75^75^75^ (2^100 times) mod 17
Source: VTRMC 2010 P2
May 17, 2021
number theory
Problem Statement
For
n
n
n
a positive integer, define
f
1
(
n
)
=
n
f_1(n)=n
f
1
(
n
)
=
n
and then for
i
i
i
a positive integer, define
f
i
+
1
(
n
)
=
f
i
(
n
)
f
i
(
n
)
f_{i+1}(n)=f_i(n)^{f_i(n)}
f
i
+
1
(
n
)
=
f
i
(
n
)
f
i
(
n
)
. Determine
f
100
(
75
)
(
m
o
d
17
)
f_{100}(75)\pmod{17}
f
100
(
75
)
(
mod
17
)
. Justify your answer.
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