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International Contests
Nordic
2003 Nordic
4
4
Part of
2003 Nordic
Problems
(1)
f(x) + f(y) = f(xy f(x + y))
Source: Nordic Mathematical Contest 2003 #4
9/24/2017
Let
R
∗
=
R
−
{
0
}
{R^* = R-\{0\}}
R
∗
=
R
−
{
0
}
be the set of non-zero real numbers. Find all functions
f
:
R
∗
→
R
∗
{f : R^* \rightarrow R^*}
f
:
R
∗
→
R
∗
satisfying
f
(
x
)
+
f
(
y
)
=
f
(
x
y
f
(
x
+
y
)
)
{f(x) + f(y) = f(xy f(x + y))}
f
(
x
)
+
f
(
y
)
=
f
(
x
y
f
(
x
+
y
))
, for
x
,
y
∈
R
∗
{x, y \in R^*}
x
,
y
∈
R
∗
and
x
+
y
≠
0
{ x + y\ne 0 }
x
+
y
=
0
.
functional equation
algebra