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Olympic Revenge
2005 Olympic Revenge
3
Find the function!
Find the function!
Source: Problem 3, Brazilian Olympic Revenge 2005
June 1, 2005
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
:
R
→
R
f: R \rightarrow R
f
:
R
→
R
such that
f
(
x
+
y
f
(
x
)
)
+
f
(
x
f
(
y
)
−
y
)
=
f
(
x
)
−
f
(
y
)
+
2
x
y
f(x+yf(x))+f(xf(y)-y)=f(x)-f(y)+2xy
f
(
x
+
y
f
(
x
))
+
f
(
x
f
(
y
)
−
y
)
=
f
(
x
)
−
f
(
y
)
+
2
x
y
for all
x
,
y
∈
R
x,y \in R
x
,
y
∈
R
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