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Niels Henrik Abels Math Contest (Norwegian Math Olympiad) Final Round
2024 Abelkonkurransen Finale
2b
2b
Part of
2024 Abelkonkurransen Finale
Problems
(1)
Standard functional equation from R to R
Source: Abelkonkurransen Finale 2024, Problem 2b
3/8/2024
Find all functions
f
:
R
→
R
f:\mathbb{R} \to \mathbb{R}
f
:
R
→
R
satisfying
x
f
(
f
(
x
)
+
y
)
=
f
(
x
y
)
+
x
2
xf(f(x)+y)=f(xy)+x^2
x
f
(
f
(
x
)
+
y
)
=
f
(
x
y
)
+
x
2
for all
x
,
y
∈
R
x,y \in \mathbb{R}
x
,
y
∈
R
.
algebra
functional equation
algebra proposed