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2013 Pan African
2
Functional: f(x)f(y)+f(x+y)=xy
Functional: f(x)f(y)+f(x+y)=xy
Source: Pan African MO 2013 Q2
June 30, 2013
function
algebra unsolved
algebra
functional equation
Problem Statement
Find all functions
f
:
R
ā
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
ā
R
such that
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 real numbers
x
x
x
and
y
y
y
.
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