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2001 Korea Junior Math Olympiad
5
2001 KJMO P5
2001 KJMO P5
Source: 2001 KJMO P5
June 29, 2024
KJMO
Sets
set theory
combinatorics
Problem Statement
A
A
A
is a set satisfying the following the condition. Show that
2001
+
2001
2001+\sqrt{2001}
2001
+
2001
is an element of
A
A
A
.Condition (1)
1
∈
A
1 \in A
1
∈
A
(2) If
x
∈
A
x \in A
x
∈
A
, then
x
2
∈
A
x^2 \in A
x
2
∈
A
.(3) If
(
x
−
3
)
2
∈
A
(x-3)^2 \in A
(
x
−
3
)
2
∈
A
, then
x
∈
A
x \in A
x
∈
A
.
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