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EGMO
2021 EGMO
2
2
Part of
2021 EGMO
Problems
(1)
2021 EGMO P2: f(xf(x)+y) = f(y) + x^2 for rational x, y
Source: 2021 EGMO P2
4/13/2021
Find all functions
f
:
Q
ā
Q
f:\mathbb{Q}\to\mathbb{Q}
f
:
Q
ā
Q
such that the equation
f
(
x
f
(
x
)
+
y
)
=
f
(
y
)
+
x
2
f(xf(x)+y) = f(y) + x^2
f
(
x
f
(
x
)
+
y
)
=
f
(
y
)
+
x
2
holds for all rational numbers
x
x
x
and
y
y
y
.Here,
Q
\mathbb{Q}
Q
denotes the set of rational numbers.
EGMO
functional equation
EGMO 2021