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National and Regional Contests
Germany Contests
Germany Team Selection Test
2019 Germany Team Selection Test
2019 Germany Team Selection Test
Part of
Germany Team Selection Test
Subcontests
(2)
1
1
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A Problem Like A1
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
+
2
1
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Another Perspective to A3
Does there exist a subset
M
M
M
of positive integers such that for all positive rational numbers
r
<
1
r<1
r
<
1
there exists exactly one finite subset of
M
M
M
like
S
S
S
such that sum of reciprocals of elements in
S
S
S
equals
r
r
r
.