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2019 CMIMC
9
2019 T9: Multiplicative Bijection on the Naturals
2019 T9: Multiplicative Bijection on the Naturals
Source:
January 27, 2019
2019
team
Problem Statement
Let
f
:
N
→
N
f:\mathbb{N}\to \mathbb{N}
f
:
N
→
N
be a bijection satisfying
f
(
a
b
)
=
f
(
a
)
f
(
b
)
f(ab)=f(a)f(b)
f
(
ab
)
=
f
(
a
)
f
(
b
)
for all
a
,
b
∈
N
a,b\in \mathbb{N}
a
,
b
∈
N
. Determine the minimum possible value of
f
(
n
)
/
n
f(n)/n
f
(
n
)
/
n
, taken over all possible
f
f
f
and all
n
≤
2019
n\leq 2019
n
≤
2019
.
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