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Malaysia Contests
Malaysian APMO Camp Selection Test
2024 Malaysian APMO Camp Selection Test
3
3
Part of
2024 Malaysian APMO Camp Selection Test
Problems
(1)
f(x-f(y))=f(f(y))+f(x-2y)
Source: Own. Malaysian APMO CST 2024 P3
2/24/2024
Find all functions
f
:
Z
→
Z
f:\mathbb{Z}\rightarrow \mathbb{Z}
f
:
Z
→
Z
such that for all integers
x
x
x
,
y
y
y
,
f
(
x
−
f
(
y
)
)
=
f
(
f
(
y
)
)
+
f
(
x
−
2
y
)
f(x-f(y))=f(f(y))+f(x-2y)
f
(
x
−
f
(
y
))
=
f
(
f
(
y
))
+
f
(
x
−
2
y
)
Proposed by Ivan Chan Kai Chin
algebra