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National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1994 Moldova Team Selection Test
8
8
Part of
1994 Moldova Team Selection Test
Problems
(1)
f(z)+f(wz+a)=g(z)
Source: Moldova TST 1994
8/8/2023
Let
g
:
C
→
C
g: \mathbb{C} \rightarrow \mathbb{C}
g
:
C
→
C
be a function,
w
∈
C
w\in\mathbb{C}
w
∈
C
and
w
3
=
1
w^3=1
w
3
=
1
. Show that there exists a function
f
:
C
→
C
f:\mathbb{C} \rightarrow \mathbb{C}
f
:
C
→
C
such that
f
(
z
)
+
f
(
w
z
+
a
)
=
g
(
z
)
,
∀
z
∈
C
f(z)+f(wz+a)=g(z), \forall z\in\mathbb{C}
f
(
z
)
+
f
(
w
z
+
a
)
=
g
(
z
)
,
∀
z
∈
C
. When there is an unique function
f
f
f
with this property? Find it.
function