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2024 Argentina IberoAmerican TST
Problem 5
Classic FE
Classic FE
Source: Argentina IberoAmerican TST 2024 P5
August 9, 2024
algebra
functional equation
TST
Problem Statement
Find all functions
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
(
x
2
−
y
2
)
f
(
x
y
)
=
x
f
(
x
2
y
)
−
y
f
(
x
y
2
)
(x^2-y^2)f(xy)=xf(x^2y)-yf(xy^2)
(
x
2
−
y
2
)
f
(
x
y
)
=
x
f
(
x
2
y
)
−
y
f
(
x
y
2
)
for all real numbers
x
,
y
x, y
x
,
y
.
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