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Russian TST 2022
P2
Interesting FE
Interesting FE
Source: Russian TST 2022, Day 3 P2
March 21, 2023
functional equation
algebra
TST
Problem Statement
Determine all functions
f
:
R
ā
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
ā
R
satisfying
f
(
x
y
+
f
(
x
)
)
+
f
(
y
)
=
x
f
(
y
)
+
f
(
x
+
y
)
,
f(xy+f(x))+f(y)=xf(y)+f(x+y),
f
(
x
y
+
f
(
x
))
+
f
(
y
)
=
x
f
(
y
)
+
f
(
x
+
y
)
,
for all real numbers
x
,
y
x,y
x
,
y
.
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