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Bundeswettbewerb Mathematik
2006 Bundeswettbewerb Mathematik
2
functional eq from positive rationals
functional eq from positive rationals
Source:
March 5, 2007
function
induction
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
Q
+
→
R
f: Q^{+}\rightarrow R
f
:
Q
+
→
R
such that
f
(
x
)
+
f
(
y
)
+
2
x
y
f
(
x
y
)
=
f
(
x
y
)
f
(
x
+
y
)
f(x)+f(y)+2xyf(xy)=\frac{f(xy)}{f(x+y)}
f
(
x
)
+
f
(
y
)
+
2
x
y
f
(
x
y
)
=
f
(
x
+
y
)
f
(
x
y
)
for all
x
,
y
∈
Q
+
x,y\in Q^{+}
x
,
y
∈
Q
+
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