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Kvant 2019
M2562
M2562
Part of
Kvant 2019
Problems
(1)
Functional equation from R^2 to R
Source: All-Russian Olympiad 2019 grade 10 problem 1
4/23/2019
Each point
A
A
A
in the plane is assigned a real number
f
(
A
)
.
f(A).
f
(
A
)
.
It is known that
f
(
M
)
=
f
(
A
)
+
f
(
B
)
+
f
(
C
)
,
f(M)=f(A)+f(B)+f(C),
f
(
M
)
=
f
(
A
)
+
f
(
B
)
+
f
(
C
)
,
whenever
M
M
M
is the centroid of
△
A
B
C
.
\triangle ABC.
△
A
BC
.
Prove that
f
(
A
)
=
0
f(A)=0
f
(
A
)
=
0
for all points
A
.
A.
A
.
algebra
functional equation