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Czech-Polish-Slovak Match
2012 Czech-Polish-Slovak Match
2
f(x + f(y)) - f(x) = (x + f(y))^4 - x^4
f(x + f(y)) - f(x) = (x + f(y))^4 - x^4
Source:
April 12, 2013
function
algebra
polynomial
algebra unsolved
Problem Statement
Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
satisfying
f
(
x
+
f
(
y
)
)
−
f
(
x
)
=
(
x
+
f
(
y
)
)
4
−
x
4
f(x+f(y))-f(x)=(x+f(y))^4-x^4
f
(
x
+
f
(
y
))
−
f
(
x
)
=
(
x
+
f
(
y
)
)
4
−
x
4
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
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