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Balkan MO
2023 Balkan MO
1
1
Part of
2023 Balkan MO
Problems
(1)
Functional xf(x+f(y))=(y-x)f(f(x)) for all reals x,y
Source: BMO 2023 Problem 1
5/10/2023
Find all functions
f
:
R
→
R
f\colon \mathbb{R} \rightarrow \mathbb{R}
f
:
R
→
R
such that for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
,
x
f
(
x
+
f
(
y
)
)
=
(
y
−
x
)
f
(
f
(
x
)
)
.
xf(x+f(y))=(y-x)f(f(x)).
x
f
(
x
+
f
(
y
))
=
(
y
−
x
)
f
(
f
(
x
))
.
Proposed by Nikola Velov, Macedonia
algebra
functional equation
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