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National and Regional Contests
PEN Problems
PEN N Problems
8
8
Part of
PEN N Problems
Problems
(1)
N 8
Source:
5/25/2007
An integer sequence
{
a
n
}
n
≥
1
\{a_{n}\}_{n \ge 1}
{
a
n
}
n
≥
1
is given such that
2
n
=
∑
d
∣
n
a
d
2^{n}=\sum^{}_{d \vert n}a_{d}
2
n
=
d
∣
n
∑
a
d
for all
n
∈
N
n \in \mathbb{N}
n
∈
N
. Show that
a
n
a_{n}
a
n
is divisible by
n
n
n
for all
n
∈
N
n \in \mathbb{N}
n
∈
N
.
Euler
modular arithmetic
geometry
geometric transformation
rotation
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