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Balkan MO Shortlist
2022 Balkan MO Shortlist
A4
Wrapped FE
Wrapped FE
Source: BMO Shortlist 2022, A4
May 13, 2023
algebra
functional equation
AZE BMO TST
AZE EGMO TST
BMO Shortlist
Problem Statement
Find all functions
f
:
R
→
R
f : \mathbb{R} \to\mathbb{R}
f
:
R
→
R
such that
f
(
0
)
≠
0
f(0)\neq 0
f
(
0
)
=
0
and
f
(
f
(
x
)
)
+
f
(
f
(
y
)
)
=
f
(
x
+
y
)
f
(
x
y
)
,
f(f(x)) + f(f(y)) = f(x + y)f(xy),
f
(
f
(
x
))
+
f
(
f
(
y
))
=
f
(
x
+
y
)
f
(
x
y
)
,
for all
x
,
y
∈
R
x, y \in\mathbb{R}
x
,
y
∈
R
.
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