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PEN S Problems
13
S 13
S 13
Source:
May 25, 2007
function
inequalities
induction
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pen
Problem Statement
The sum of the digits of a natural number
n
n
n
is denoted by
S
(
n
)
S(n)
S
(
n
)
. Prove that
S
(
8
n
)
≥
1
8
S
(
n
)
S(8n) \ge \frac{1}{8} S(n)
S
(
8
n
)
≥
8
1
S
(
n
)
for each
n
n
n
.
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