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Problems
Contests
National and Regional Contests
PEN Problems
PEN J Problems
8
8
Part of
PEN J Problems
Problems
(1)
J 8
Source:
5/25/2007
Prove that for any
δ
∈
[
0
,
1
]
\delta\in[0,1]
δ
∈
[
0
,
1
]
and any
ε
>
0
\varepsilon>0
ε
>
0
, there is an
n
∈
N
n\in\mathbb{N}
n
∈
N
such that
∣
ϕ
(
n
)
n
−
δ
∣
<
ε
\left |\frac{\phi (n)}{n}-\delta\right| <\varepsilon
n
ϕ
(
n
)
−
δ
<
ε
.
logarithms
Divisor Functions