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National and Regional Contests
Lithuania Contests
Grand Duchy of Lithuania
2014 Grand Duchy of Lithuania
4
4
Part of
2014 Grand Duchy of Lithuania
Problems
(1)
Easy problem
Source: 6th Mathematical Contest of Grand Duchy of Lithuania
10/5/2014
Determine all positive integers
n
>
1
n > 1
n
>
1
for which
n
+
D
(
n
)
n + D(n)
n
+
D
(
n
)
is a power of
10
10
10
, where
D
(
n
)
D(n)
D
(
n
)
denotes the largest integer divisor of
n
n
n
satisfying
D
(
n
)
<
n
D(n) < n
D
(
n
)
<
n
.
number theory proposed
number theory