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Nordic
2023 Nordic
P2
FE with gcd
FE with gcd
Source: Nordic MC 2023 P2
April 21, 2023
number theory
greatest common divisor
Problem Statement
Find all functions
f
:
N
→
N
f: \mathbb{N} \to \mathbb{N}
f
:
N
→
N
such that
gcd
(
f
(
x
)
,
y
)
f
(
x
y
)
=
f
(
x
)
f
(
y
)
\gcd(f(x),y)f(xy)=f(x)f(y)
g
cd
(
f
(
x
)
,
y
)
f
(
x
y
)
=
f
(
x
)
f
(
y
)
for all positive integers
x
,
y
x, y
x
,
y
.
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