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2019 Germany Team Selection Test
1
A Problem Like A1
A Problem Like A1
Source: Germany VAIMO 2019 P1
April 15, 2020
algebra
functional equation
Problem Statement
Let
Q
+
\mathbb{Q}^+
Q
+
denote the set of all positive rational numbers. Determine all functions
f
:
Q
+
→
Q
+
f:\mathbb{Q}^+\to \mathbb{Q}^+
f
:
Q
+
→
Q
+
satisfying
f
(
x
2
f
(
y
)
2
)
=
f
(
x
2
)
f
(
y
)
f(x^2f(y)^2)=f(x^2)f(y)
f
(
x
2
f
(
y
)
2
)
=
f
(
x
2
)
f
(
y
)
for all
x
,
y
∈
Q
+
x,y\in\mathbb{Q}^+
x
,
y
∈
Q
+
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