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Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2015 Dutch BxMO/EGMO TST
5
5
Part of
2015 Dutch BxMO/EGMO TST
Problems
(1)
(x^2 + y^2)f(xy) = f(x)f(y)f(x^2 + y^2)
Source: Dutch BxMO/EGMO TST 2015 p5
8/24/2019
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
.
algebra
functional equation