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National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2010 Dutch BxMO TST
2
fuctional in R, f(x)f(y) = f(x + y) + xy
fuctional in R, f(x)f(y) = f(x + y) + xy
Source: Dutch BxMO TST 2010 p2
August 24, 2019
Problem Statement
Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
satisfying
f
(
x
)
f
(
y
)
=
f
(
x
+
y
)
+
x
y
f(x)f(y) = f(x + y) + xy
f
(
x
)
f
(
y
)
=
f
(
x
+
y
)
+
x
y
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
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