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2024-IMOC
N6
N6
Part of
2024-IMOC
Problems
(1)
Rational NT FE
Source: 2024 IMOC N6 (Night 4)
8/8/2024
Find all functions
f
:
Q
+
→
Q
+
f:\mathbb{Q}^+\to\mathbb{Q}^+
f
:
Q
+
→
Q
+
such that
x
y
(
f
(
x
)
−
f
(
y
)
)
∣
x
−
f
(
f
(
y
)
)
xy(f(x)-f(y))|x-f(f(y))
x
y
(
f
(
x
)
−
f
(
y
))
∣
x
−
f
(
f
(
y
))
holds for all positive rationals
x
x
x
,
y
y
y
(we define that
a
∣
b
a|b
a
∣
b
if and only if exist
n
∈
Z
n \in \mathbb{Z}
n
∈
Z
such that
b
=
a
n
b=an
b
=
an
) Proposed by supercarry & windleaf1A
number theory
functional equation