MathDB
Problems
Contests
National and Regional Contests
North Macedonia Contests
Macedonian Team Selection Test
2023 Macedonian Team Selection Test
Problem 4
Problem 4
Part of
2023 Macedonian Team Selection Test
Problems
(1)
Similar to BMO SL 2022 A6
Source: 2023 Macedonian Team Selection Test P4
5/21/2023
Let
f
:
R
2
→
R
f: \mathbb{R}^2 \to \mathbb{R}
f
:
R
2
→
R
be a function satisfying the following property: If
A
,
B
,
C
∈
R
2
A, B, C \in \mathbb{R}^2
A
,
B
,
C
∈
R
2
are the vertices of an equilateral triangle with sides of length
1
1
1
, then
f
(
A
)
+
f
(
B
)
+
f
(
C
)
=
0.
f(A) + f(B) + f(C) = 0.
f
(
A
)
+
f
(
B
)
+
f
(
C
)
=
0.
Show that
f
(
x
)
=
0
f(x) = 0
f
(
x
)
=
0
for all
x
∈
R
2
x \in \mathbb{R}^2
x
∈
R
2
.Proposed by Ilir Snopce
geometry