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Macedonia National Olympiad 2011 - Problem 4
Macedonia National Olympiad 2011 - Problem 4
Source:
April 16, 2011
function
search
algebra unsolved
algebra
Problem Statement
Find all functions
~
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
~
which satisfy the equation
f
(
x
+
y
f
(
x
)
)
=
f
(
f
(
x
)
)
+
x
f
(
y
)
.
f(x+yf(x))\, =\, f(f(x)) + xf(y)\, .
f
(
x
+
y
f
(
x
))
=
f
(
f
(
x
))
+
x
f
(
y
)
.
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