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Vojtěch Jarník IMC
2000 VJIMC
Problem 2
n^(0.5*d(n)) is injective
n^(0.5*d(n)) is injective
Source: VJIMC 2000 1.2
July 27, 2021
number theory
function
Problem Statement
Let
f
:
N
→
R
f:\mathbb N\to\mathbb R
f
:
N
→
R
be given by
f
(
n
)
=
n
1
2
τ
(
n
)
f(n)=n^{\frac12\tau(n)}
f
(
n
)
=
n
2
1
τ
(
n
)
for
n
∈
N
=
{
1
,
2
,
…
}
n\in\mathbb N=\{1,2,\ldots\}
n
∈
N
=
{
1
,
2
,
…
}
where
τ
(
n
)
\tau(n)
τ
(
n
)
is the number of divisors of
n
n
n
. Show that
f
f
f
is an injection.
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