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Problems
Contests
National and Regional Contests
Hungary Contests
Kürschák Math Competition
1992 Kurschak Competition
2
2
Part of
1992 Kurschak Competition
Problems
(1)
Digital sum squared
Source: Kürschák 1992, problem 2
7/20/2014
For any positive integer
k
k
k
define
f
1
(
k
)
f_1(k)
f
1
(
k
)
as the square of the digital sum of
k
k
k
in the decimal system, and
f
n
(
k
)
=
f
1
(
f
n
−
1
(
k
)
)
f_{n}(k)=f_1(f_{n-1}(k))
f
n
(
k
)
=
f
1
(
f
n
−
1
(
k
))
∀
n
>
1
\forall n>1
∀
n
>
1
. Compute
f
1992
(
2
1991
)
f_{1992}(2^{1991})
f
1992
(
2
1991
)
.
modular arithmetic
number theory unsolved
number theory