MathDB
Problems
Contests
National and Regional Contests
Taiwan Contests
IMOC Shortlist
2020-IMOC
N5
N5
Part of
2020-IMOC
Problems
(1)
FE on Famous Identity
Source: IMOC 2020
9/3/2020
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N
5.
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<span class='latex-bold'>N5.</span>
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N
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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
functional equation
number theory
IMOC
Taiwan