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National and Regional Contests
PEN Problems
PEN S Problems
36
36
Part of
PEN S Problems
Problems
(1)
S 36
Source:
5/25/2007
For every natural number
n
n
n
, denote
Q
(
n
)
Q(n)
Q
(
n
)
the sum of the digits in the decimal representation of
n
n
n
. Prove that there are infinitely many natural numbers
k
k
k
with
Q
(
3
k
)
>
Q
(
3
k
+
1
)
Q(3^{k})>Q(3^{k+1})
Q
(
3
k
)
>
Q
(
3
k
+
1
)
.
modular arithmetic
induction
limit
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