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National and Regional Contests
Lithuania Contests
Grand Duchy of Lithuania
2023 Grand Duchy of Lithuania
1
1
Part of
2023 Grand Duchy of Lithuania
Problems
(1)
f(f(x + y)) = f(x + y) + f(x)f(y) + axy
Source: 2023 Grand Duchy of Lithuania, MC p1 (Baltic Way TST)
3/23/2024
Given a non-zero real number
a
a
a
. Find all functions
f
:
R
→
R
f : R \to R
f
:
R
→
R
, such that
f
(
f
(
x
+
y
)
)
=
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
+
a
x
y
f(f(x + y)) = f(x + y) + f(x)f(y) + axy
f
(
f
(
x
+
y
))
=
f
(
x
+
y
)
+
f
(
x
)
f
(
y
)
+
a
x
y
for all
x
,
y
∈
R
x, y \in R
x
,
y
∈
R
.
functional equation
algebra