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2023-IMOC
N4
Perfect square NT FE
Perfect square NT FE
Source: IMOC 2023 N4
September 9, 2023
number theory
Problem Statement
Find all functions
f
:
N
ā
N
f:\mathbb{N} \rightarrow \mathbb{N}
f
:
N
ā
N
, such that
a
f
(
a
)
3
+
2
a
b
f
(
a
)
+
b
f
(
b
)
af(a)^3+2abf(a)+bf(b)
a
f
(
a
)
3
+
2
ab
f
(
a
)
+
b
f
(
b
)
is a perfect square for all positive integers
a
,
b
a,b
a
,
b
.
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