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Pan-African Shortlist
2018 Pan-African Shortlist
A5
A5
Part of
2018 Pan-African Shortlist
Problems
(1)
2018 PAMO Shortlist: Completely multiplicative involution on the natural numbers
Source: 2018 Pan-African Shortlist - A5
5/6/2019
Let
g
:
N
→
N
g : \mathbb{N} \to \mathbb{N}
g
:
N
→
N
be a function satisfying: [*]
g
(
x
y
)
=
g
(
x
)
g
(
y
)
g(xy) = g(x)g(y)
g
(
x
y
)
=
g
(
x
)
g
(
y
)
for all
x
,
y
∈
N
x, y \in \mathbb{N}
x
,
y
∈
N
, [*]
g
(
g
(
x
)
)
=
x
g(g(x)) = x
g
(
g
(
x
))
=
x
for all
x
∈
N
x \in \mathbb{N}
x
∈
N
, and [*]
g
(
x
)
≠
x
g(x) \neq x
g
(
x
)
=
x
for
2
≤
x
≤
2018
2 \leq x \leq 2018
2
≤
x
≤
2018
.Find the minimum possible value of
g
(
2
)
g(2)
g
(
2
)
.
number theory
algebra
function
functional equation
multiplicative function