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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2018 Iran MO (2nd Round)
4
Functional Equation
Functional Equation
Source: Iran MO 2018, second round, day 2, P4
April 27, 2018
algebra
function
functional equation
Problem Statement
Find all functions
f
:
R
→
R
f:\Bbb {R} \rightarrow \Bbb {R}
f
:
R
→
R
such that:
f
(
x
+
y
)
f
(
x
2
−
x
y
+
y
2
)
=
x
3
+
y
3
f(x+y)f(x^2-xy+y^2)=x^3+y^3
f
(
x
+
y
)
f
(
x
2
−
x
y
+
y
2
)
=
x
3
+
y
3
for all reals
x
,
y
x, y
x
,
y
.
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