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Baltic Way
2008 Baltic Way
10
10
Part of
2008 Baltic Way
Problems
(1)
Sum of digits...
Source: Baltic Way 2008, Problem 10
11/23/2008
For a positive integer
n
n
n
, let
S
(
n
)
S(n)
S
(
n
)
denote the sum of its digits. Find the largest possible value of the expression
S
(
n
)
S
(
16
n
)
\frac {S(n)}{S(16n)}
S
(
16
n
)
S
(
n
)
.
number theory unsolved
number theory