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Belarus Team Selection Test
2024 Belarus Team Selection Test
3.2
3.2
Part of
2024 Belarus Team Selection Test
Problems
(1)
Easiest FE ever
Source: Belarus TST 2024
7/17/2024
Find all functions
f
:
R
→
R
f: \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that for any reals
x
≠
y
x \neq y
x
=
y
the following equality is true:
f
(
x
+
y
)
2
=
f
(
x
+
y
)
+
f
(
x
)
+
f
(
y
)
f(x+y)^2=f(x+y)+f(x)+f(y)
f
(
x
+
y
)
2
=
f
(
x
+
y
)
+
f
(
x
)
+
f
(
y
)
D. Zmiaikou
functional equation
algebra
TST