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National and Regional Contests
Taiwan Contests
TST Round 2
2022 Taiwan TST Round 2
A
A
Part of
2022 Taiwan TST Round 2
Problems
(1)
A hard functional equation in Taiwan TST
Source: 2022 Taiwan TST Round 2 Independent Study 2-A
4/8/2022
Determine all functions
f
:
R
+
ā
R
+
f: \mathbb{R}^+ \to \mathbb{R}^+
f
:
R
+
ā
R
+
satisfying
f
(
x
+
y
2
f
(
y
)
)
=
f
(
1
+
y
f
(
x
)
)
f
(
x
)
f\bigl(x + y^2 f(y)\bigr) = f\bigl(1 + yf(x)\bigr)f(x)
f
(
x
+
y
2
f
(
y
)
)
=
f
(
1
+
y
f
(
x
)
)
f
(
x
)
for any positive reals
x
x
x
,
y
y
y
, where
R
+
\mathbb{R}^+
R
+
is the collection of all positive real numbers. Proposed by Ming Hsiao.
algebra
functional equation
ming
Taiwan