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Middle European Mathematical Olympiad
2016 Middle European Mathematical Olympiad
2
functional equation on reals with y-x
functional equation on reals with y-x
Source: MEMO 2016 T2
August 25, 2016
algebra
functional equation
algebra proposed
Problem Statement
Let
R
\mathbb{R}
R
denote the set of the reals. Find all
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that
f
(
x
)
f
(
y
)
=
x
f
(
f
(
y
−
x
)
)
+
x
f
(
2
x
)
+
f
(
x
2
)
f(x)f(y) = xf(f(y-x)) + xf(2x) + f(x^2)
f
(
x
)
f
(
y
)
=
x
f
(
f
(
y
−
x
))
+
x
f
(
2
x
)
+
f
(
x
2
)
for all real
x
,
y
x, y
x
,
y
.
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