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2011 Nordic
3
Functional: f(f(x)+y)=f(x^2-y)+4yf(x)
Functional: f(f(x)+y)=f(x^2-y)+4yf(x)
Source: Nordic MO 2011 Q3
April 21, 2013
function
algebra unsolved
algebra
Problem Statement
Find all functions
f
f
f
such that
f
(
f
(
x
)
+
y
)
=
f
(
x
2
ā
y
)
+
4
y
f
(
x
)
f(f(x) + y) = f(x^2-y) + 4yf(x)
f
(
f
(
x
)
+
y
)
=
f
(
x
2
ā
y
)
+
4
y
f
(
x
)
for all real numbers
x
x
x
and
y
y
y
.
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