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1993 Turkey Team Selection Test
6
Functional equation from Q^+ to Q^+
Functional equation from Q^+ to Q^+
Source: Turkey IMO TST 1993 #6
July 7, 2011
function
algebra unsolved
algebra
Problem Statement
Determine all functions
f
:
Q
+
→
Q
+
f: \mathbb{Q^+} \rightarrow \mathbb{Q^+}
f
:
Q
+
→
Q
+
that satisfy:
f
(
x
+
y
x
)
=
f
(
x
)
+
f
(
y
x
)
+
2
y
for all
x
,
y
∈
Q
+
f\left(x+\frac{y}{x}\right) = f(x)+f\left(\frac{y}{x}\right)+2y \:\text{for all}\: x, y \in \mathbb{Q^+}
f
(
x
+
x
y
)
=
f
(
x
)
+
f
(
x
y
)
+
2
y
for all
x
,
y
∈
Q
+
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