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2023 Indonesia MO
2
2
Part of
2023 Indonesia MO
Problems
(1)
Simple FE on National Contest
Source: INAMO 2023 P2 (OSN 2023)
8/29/2023
Determine all functions
f
:
R
→
R
f : \mathbb{R} \to \mathbb{R}
f
:
R
→
R
such that the following equation holds for every real
x
,
y
x,y
x
,
y
:
f
(
f
(
x
)
+
y
)
=
⌊
x
+
f
(
f
(
y
)
)
⌋
.
f(f(x) + y) = \lfloor x + f(f(y)) \rfloor.
f
(
f
(
x
)
+
y
)
=
⌊
x
+
f
(
f
(
y
))⌋
.
Note:
⌊
x
⌋
\lfloor x \rfloor
⌊
x
⌋
denotes the greatest integer not greater than
x
x
x
.
functional equation
algebra
floor function
Floor
Indonesia