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Romanian Masters of Mathematics Collection
2019 Romanian Master of Mathematics Shortlist
A1
f(a)=a,-a
f(a)=a,-a
Source: RMMSL-19 A1
May 27, 2020
algebra
RMM Shortlist
Problem Statement
Determine all the functions
f
:
R
↦
R
f:\mathbb R\mapsto\mathbb R
f
:
R
↦
R
satisfies the equation
f
(
a
2
+
a
b
+
f
(
b
2
)
)
=
a
f
(
b
)
+
b
2
+
f
(
a
2
)
∀
a
,
b
∈
R
f(a^2 +ab+ f(b^2))=af(b)+b^2+ f(a^2)\,\forall a,b\in\mathbb R
f
(
a
2
+
ab
+
f
(
b
2
))
=
a
f
(
b
)
+
b
2
+
f
(
a
2
)
∀
a
,
b
∈
R
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