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Albania IMO Selection
Albania IMO Selection
Source:
May 25, 2013
function
algebra
functional equation
algebra unsolved
Problem Statement
Solve the function
f
:
ℜ
→
ℜ
f: \Re \to \Re
f
:
ℜ
→
ℜ
:
f
(
x
3
)
+
f
(
y
3
)
=
(
x
+
y
)
(
f
(
x
2
)
+
f
(
y
2
)
−
f
(
x
y
)
)
f( x^{3} )+ f(y^{3}) = (x+y)(f(x^{2} )+f(y^{2} )-f(xy))
f
(
x
3
)
+
f
(
y
3
)
=
(
x
+
y
)
(
f
(
x
2
)
+
f
(
y
2
)
−
f
(
x
y
))
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