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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2015 Dutch BxMO/EGMO TST
5
(x^2 + y^2)f(xy) = f(x)f(y)f(x^2 + y^2)
(x^2 + y^2)f(xy) = f(x)f(y)f(x^2 + y^2)
Source: Dutch BxMO/EGMO TST 2015 p5
August 24, 2019
algebra
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f : R \to R
f
:
R
ā
R
satisfying
(
x
2
+
y
2
)
f
(
x
y
)
=
f
(
x
)
f
(
y
)
f
(
x
2
+
y
2
)
(x^2 + y^2)f(xy) = f(x)f(y)f(x^2 + y^2)
(
x
2
+
y
2
)
f
(
x
y
)
=
f
(
x
)
f
(
y
)
f
(
x
2
+
y
2
)
for all real numbers
x
x
x
and
y
y
y
.
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