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Akdeniz University MO
1997 Akdeniz University MO
3
9 $\mid n$ :D
9 $\mid n$ :D
Source:
January 30, 2016
number theory
Problem Statement
Let for all
k
∈
N
k \in {\mathbb N}
k
∈
N
k
k
k
's sum of the digits is
T
(
k
)
T(k)
T
(
k
)
. If a natural number
n
n
n
such that
T
(
n
)
=
T
(
1997
n
)
T(n)=T(1997n)
T
(
n
)
=
T
(
1997
n
)
, prove that
9
∣
n
9\mid n
9
∣
n
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