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Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2020-IMOC
N5
FE on Famous Identity
FE on Famous Identity
Source: IMOC 2020
September 3, 2020
functional equation
number theory
IMOC
Taiwan
Problem Statement
<
s
p
a
n
c
l
a
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s
=
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l
a
t
e
x
−
b
o
l
d
′
>
N
5.
<
/
s
p
a
n
>
<span class='latex-bold'>N5.</span>
<
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an
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a
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N
5.
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Find all
f
:
N
→
N
f: \mathbb{N} \rightarrow \mathbb{N}
f
:
N
→
N
such that for all
a
,
b
,
c
∈
N
a,b,c \in \mathbb{N}
a
,
b
,
c
∈
N
f
(
a
)
+
f
(
b
)
+
f
(
c
)
−
a
b
−
b
c
−
c
a
∣
a
f
(
a
)
+
b
f
(
b
)
+
c
f
(
c
)
−
3
a
b
c
f(a)+f(b)+f(c)-ab-bc-ca \mid af(a)+bf(b)+cf(c)-3abc
f
(
a
)
+
f
(
b
)
+
f
(
c
)
−
ab
−
b
c
−
c
a
∣
a
f
(
a
)
+
b
f
(
b
)
+
c
f
(
c
)
−
3
ab
c
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