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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2021 Korea Junior Math Olympiad
5
5
Part of
2021 Korea Junior Math Olympiad
Problems
(1)
Korean Functional Equation With Square
Source: KJMO 2021 P5
11/13/2021
Determine all functions
f
:
R
→
R
f \colon \mathbb{R} \to \mathbb{R}
f
:
R
→
R
satisfying
f
(
f
(
x
+
y
)
−
f
(
x
−
y
)
)
=
y
2
f
(
x
)
f(f(x+y)-f(x-y))=y^2f(x)
f
(
f
(
x
+
y
)
−
f
(
x
−
y
))
=
y
2
f
(
x
)
for all
x
,
y
∈
R
x, y \in \mathbb{R}
x
,
y
∈
R
.
functional equation
algebra