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National and Regional Contests
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Dutch IMO TST
2023 Dutch IMO TST
4
4
Part of
2023 Dutch IMO TST
Problems
(1)
Ridiculous FE with straight bash
Source: Turkey TST 2022 P2 Day 1
3/13/2022
Find all functions
f
:
Q
+
→
Q
f: \mathbb{Q^+} \rightarrow \mathbb{Q}
f
:
Q
+
→
Q
satisfying
f
(
x
)
+
f
(
y
)
=
(
f
(
x
+
y
)
+
1
x
+
y
)
(
1
−
x
y
+
f
(
x
y
)
)
f(x)+f(y)= \left(f(x+y)+\frac{1}{x+y} \right) (1-xy+f(xy))
f
(
x
)
+
f
(
y
)
=
(
f
(
x
+
y
)
+
x
+
y
1
)
(
1
−
x
y
+
f
(
x
y
))
for all
x
,
y
∈
Q
+
x, y \in \mathbb{Q^+}
x
,
y
∈
Q
+
.
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