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China Contests
South East Mathematical Olympiad
2016 South East Mathematical Olympiad
7
find the value of $|P|$
find the value of $|P|$
Source: 2016 China South East Mathematical Olympiad Grade 11 Problem 7
August 6, 2016
number theory
Problem Statement
Let
A
=
{
a
3
+
b
3
+
c
3
−
3
a
b
c
∣
a
,
b
,
c
∈
N
}
A=\{a^3+b^3+c^3-3abc|a,b,c\in\mathbb{N}\}
A
=
{
a
3
+
b
3
+
c
3
−
3
ab
c
∣
a
,
b
,
c
∈
N
}
,
B
=
{
(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
∣
a
,
b
,
c
∈
N
}
B=\{(a+b-c)(b+c-a)(c+a-b)|a,b,c\in\mathbb{N}\}
B
=
{(
a
+
b
−
c
)
(
b
+
c
−
a
)
(
c
+
a
−
b
)
∣
a
,
b
,
c
∈
N
}
,
P
=
{
n
∣
n
∈
A
∩
B
,
1
≤
n
≤
2016
}
P=\{n|n\in A\cap B,1\le n\le 2016\}
P
=
{
n
∣
n
∈
A
∩
B
,
1
≤
n
≤
2016
}
, find the value of
∣
P
∣
|P|
∣
P
∣
.
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