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Czech-Polish-Slovak Match
2020 Czech-Austrian-Polish-Slovak Match
4
4
Part of
2020 Czech-Austrian-Polish-Slovak Match
Problems
(1)
(x+y)(f(x)-f(y))=a(x-y)f(x+y) where a given real
Source: 2020 Czech-Polish-Slovak Match p4
10/8/2020
Let
a
a
a
be a given real number. Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
such that
(
x
+
y
)
(
f
(
x
)
−
f
(
y
)
)
=
a
(
x
−
y
)
f
(
x
+
y
)
(x+y)(f(x)-f(y))=a(x-y)f(x+y)
(
x
+
y
)
(
f
(
x
)
−
f
(
y
))
=
a
(
x
−
y
)
f
(
x
+
y
)
holds for all
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
. (Walther Janous, Austria)
algebra
functional equation
functional