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International Contests
Silk Road
2004 Silk Road
1
1
Part of
2004 Silk Road
Problems
(1)
International competition SRMC 2004 P-1
Source:
9/7/2010
Find all
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
, such that
(
x
+
y
)
(
f
(
x
)
−
f
(
y
)
)
=
(
x
−
y
)
f
(
x
+
y
)
(x+y)(f(x)-f(y))=(x-y)f(x+y)
(
x
+
y
)
(
f
(
x
)
−
f
(
y
))
=
(
x
−
y
)
f
(
x
+
y
)
for all real
x
,
y
x,y
x
,
y
.
algebra proposed
algebra