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National and Regional Contests
PEN Problems
PEN S Problems
34
34
Part of
PEN S Problems
Problems
(1)
S 34
Source:
5/25/2007
Let
S
n
S_{n}
S
n
be the sum of the digits of
2
n
2^n
2
n
. Prove or disprove that
S
n
+
1
=
S
n
S_{n+1}=S_{n}
S
n
+
1
=
S
n
for some positive integer
n
n
n
.
modular arithmetic
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