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2024-IMOC
N7
|xf(y)-yf(x)| is a perfect square
|xf(y)-yf(x)| is a perfect square
Source: 2024IMOC
August 1, 2024
number theory
functional equation
Problem Statement
Find all functions
f
:
N
→
N
f:\mathbb{N}\to\mathbb{N}
f
:
N
→
N
such that
∣
x
f
(
y
)
−
y
f
(
x
)
∣
|xf(y)-yf(x)|
∣
x
f
(
y
)
−
y
f
(
x
)
∣
is a perfect square for every
x
,
y
∈
N
x,y \in \mathbb{N}
x
,
y
∈
N
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