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Problems
Contests
National and Regional Contests
PEN Problems
PEN M Problems
15
15
Part of
PEN M Problems
Problems
(1)
M 15
Source:
5/25/2007
For a given positive integer
k
k
k
denote the square of the sum of its digits by
f
1
(
k
)
f_{1}(k)
f
1
(
k
)
and let
f
n
+
1
(
k
)
=
f
1
(
f
n
(
k
)
)
f_{n+1}(k)=f_{1}(f_{n}(k))
f
n
+
1
(
k
)
=
f
1
(
f
n
(
k
))
. Determine the value of
f
1991
(
2
1990
)
f_{1991}(2^{1990})
f
1991
(
2
1990
)
.
logarithms
modular arithmetic
Recursive Sequences