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2016 APMO
5
5
Part of
2016 APMO
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(1)
APMO 2016: Functional equation
Source: APMO 2016, problem 5
5/16/2016
Find all functions
f
:
R
+
ā
R
+
f: \mathbb{R}^+ \to \mathbb{R}^+
f
:
R
+
ā
R
+
such that
(
z
+
1
)
f
(
x
+
y
)
=
f
(
x
f
(
z
)
+
y
)
+
f
(
y
f
(
z
)
+
x
)
,
(z + 1)f(x + y) = f(xf(z) + y) + f(yf(z) + x),
(
z
+
1
)
f
(
x
+
y
)
=
f
(
x
f
(
z
)
+
y
)
+
f
(
y
f
(
z
)
+
x
)
,
for all positive real numbers
x
,
y
,
z
x, y, z
x
,
y
,
z
.Fajar Yuliawan, Indonesia
function
functional equation
algebra
APMO