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2018-IMOC
A1
A1
Part of
2018-IMOC
Problems
(1)
rational FE in four variables
Source: IMOC 2018 A1
8/15/2021
Find all functions
f
:
Q
→
Q
f:\mathbb Q\to\mathbb Q
f
:
Q
→
Q
such that for all
x
,
y
,
z
,
w
∈
Q
x,y,z,w\in\mathbb Q
x
,
y
,
z
,
w
∈
Q
,
f
(
f
(
x
y
z
w
)
+
x
+
y
)
+
f
(
z
)
+
f
(
w
)
=
f
(
f
(
x
y
z
w
)
+
z
+
w
)
+
f
(
x
)
+
f
(
y
)
.
f(f(xyzw)+x+y)+f(z)+f(w)=f(f(xyzw)+z+w)+f(x)+f(y).
f
(
f
(
x
yz
w
)
+
x
+
y
)
+
f
(
z
)
+
f
(
w
)
=
f
(
f
(
x
yz
w
)
+
z
+
w
)
+
f
(
x
)
+
f
(
y
)
.
fe
functional equation
algebra