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National and Regional Contests
The Philippines Contests
Philippine TST
2019 Philippine TST
2
Degree 2019 functional equation
Degree 2019 functional equation
Source: 2019 Philippine IMO TST3 Problem 2
May 4, 2022
algebra
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
ā
R
that satisfy the equation
f
(
x
2019
+
y
2019
)
=
x
(
f
(
x
)
)
2018
+
y
(
f
(
y
)
)
2018
f(x^{2019} + y^{2019}) = x(f(x))^{2018} + y(f(y))^{2018}
f
(
x
2019
+
y
2019
)
=
x
(
f
(
x
)
)
2018
+
y
(
f
(
y
)
)
2018
for all real numbers
x
x
x
and
y
y
y
.
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